किसी बहुपद (p(x)) का शून्यक ज्यामितीय रूप से क्या दर्शाता है?
What does a zero of a polynomial (p(x)) represent geometrically?
#polynomials
#zeroes
#geometrical-meaning
#x-axis
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A वह बिंदु जहाँ ग्राफ (x)-अक्ष को काटता है / The point where the graph cuts the (x)-axis
B वह बिंदु जहाँ ग्राफ (y)-अक्ष को काटता है / The point where the graph cuts the (y)-axis
C ग्राफ का सबसे ऊँचा बिंदु / The highest point of the graph
D ग्राफ का सबसे निचला बिंदु / The lowest point of the graph
Explanation opens after your attempt
Correct Answer
A. वह बिंदु जहाँ ग्राफ (x)-अक्ष को काटता है / The point where the graph cuts the (x)-axis
Step 1
Concept
A zero is the (x)-value for which (p(x)=0). On the graph, it is shown where the curve meets the (x)-axis.
Step 2
Why this answer is correct
The correct answer is A. वह बिंदु जहाँ ग्राफ (x)-अक्ष को काटता है / The point where the graph cuts the (x)-axis. A zero is the (x)-value for which (p(x)=0). On the graph, it is shown where the curve meets the (x)-axis.
Step 3
Exam Tip
किसी बहुपद का शून्यक वह (x)-मान होता है जहाँ (p(x)=0) होता है। ग्राफ में यह (x)-अक्ष पर मिलने वाला बिंदु बताता है।
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यदि किसी बहुपद का ग्राफ (x)-अक्ष को (x=3) पर काटता है, तो उसका शून्यक क्या होगा?
If the graph of a polynomial cuts the (x)-axis at (x=3), what is its zero?
#polynomials
#graph
#zero
#x-intercept
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A (3)
B (-3)
C (0)
D (1)
Explanation opens after your attempt
Step 1
Concept
The (x)-value where the graph cuts the (x)-axis is the zero. Hence the zero is (3).
Step 2
Why this answer is correct
The correct answer is A. (3). The (x)-value where the graph cuts the (x)-axis is the zero. Hence the zero is (3).
Step 3
Exam Tip
जहाँ ग्राफ (x)-अक्ष को काटता है वही (x)-मान शून्यक होता है। इसलिए यहाँ शून्यक (3) है।
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यदि ग्राफ (x)-अक्ष को ((-2,0)) और ((4,0)) पर काटता है, तो बहुपद के शून्यक कौन-से हैं?
If a graph cuts the (x)-axis at ((-2,0)) and ((4,0)), what are the zeroes of the polynomial?
#x-intercepts
#zeroes
#polynomial-graph
#class-10
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A (-2) और (4) / (-2) and (4)
B (2) और (-4) / (2) and (-4)
C (0) और (4) / (0) and (4)
D (-2) और (0) / (-2) and (0)
Explanation opens after your attempt
Correct Answer
A. (-2) और (4) / (-2) and (4)
Step 1
Concept
Zeroes are the (x)-coordinates of the points where the graph meets the (x)-axis. So the zeroes are (-2) and (4).
Step 2
Why this answer is correct
The correct answer is A. (-2) और (4) / (-2) and (4). Zeroes are the (x)-coordinates of the points where the graph meets the (x)-axis. So the zeroes are (-2) and (4).
Step 3
Exam Tip
शून्यक हमेशा (x)-अक्ष पर कटने वाले बिंदुओं के (x)-निर्देशांक होते हैं। इसलिए शून्यक (-2) और (4) हैं।
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यदि किसी रैखिक बहुपद का ग्राफ (x)-अक्ष को केवल एक बार काटता है, तो उसके कितने शून्यक होंगे?
If the graph of a linear polynomial cuts the (x)-axis only once, how many zeroes will it have?
#linear-polynomial
#zeroes
#graph
#easy
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A एक / One
B दो / Two
C तीन / Three
D कोई नहीं / None
Explanation opens after your attempt
Step 1
Concept
The graph of a linear polynomial is a line and usually cuts the (x)-axis once. Therefore it has one zero.
Step 2
Why this answer is correct
The correct answer is A. एक / One. The graph of a linear polynomial is a line and usually cuts the (x)-axis once. Therefore it has one zero.
Step 3
Exam Tip
रैखिक बहुपद का ग्राफ एक रेखा होता है और सामान्यतः (x)-अक्ष को एक बार काटता है। इसलिए उसका एक शून्यक होता है।
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किस बिंदु से बहुपद का शून्यक सीधे मिल सकता है?
From which point can the zero of a polynomial be directly found?
#zeroes
#graphical-meaning
#x-axis
#polynomials
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A जहाँ ग्राफ (x)-अक्ष को छूता या काटता है / Where the graph touches or cuts the (x)-axis
B जहाँ ग्राफ (y)-अक्ष को काटता है / Where the graph cuts the (y)-axis
C जहाँ ग्राफ ऊपर जाता है / Where the graph goes upward
D जहाँ ग्राफ नीचे जाता है / Where the graph goes downward
Explanation opens after your attempt
Correct Answer
A. जहाँ ग्राफ (x)-अक्ष को छूता या काटता है / Where the graph touches or cuts the (x)-axis
Step 1
Concept
For a zero, (y=0), and this happens on the (x)-axis. So look at the points where the graph meets the (x)-axis.
Step 2
Why this answer is correct
The correct answer is A. जहाँ ग्राफ (x)-अक्ष को छूता या काटता है / Where the graph touches or cuts the (x)-axis. For a zero, (y=0), and this happens on the (x)-axis. So look at the points where the graph meets the (x)-axis.
Step 3
Exam Tip
शून्यक के लिए (y=0) होना चाहिए और यह स्थिति (x)-अक्ष पर होती है। इसलिए (x)-अक्ष से मिलने वाले बिंदु देखें।
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यदि किसी बहुपद का ग्राफ (x)-अक्ष को नहीं काटता और नहीं छूता, तो उसके वास्तविक शून्यकों की संख्या क्या होगी?
If the graph of a polynomial neither cuts nor touches the (x)-axis, how many real zeroes does it have?
#real-zeroes
#no-intersection
#polynomial-graph
#easy
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A (0)
B (1)
C (2)
D अनंत / Infinite
Explanation opens after your attempt
Step 1
Concept
Real zeroes appear only where the graph meets the (x)-axis. If it does not meet the (x)-axis, it has no real zero.
Step 2
Why this answer is correct
The correct answer is A. (0). Real zeroes appear only where the graph meets the (x)-axis. If it does not meet the (x)-axis, it has no real zero.
Step 3
Exam Tip
वास्तविक शून्यक तभी दिखते हैं जब ग्राफ (x)-अक्ष से मिले। यदि ग्राफ (x)-अक्ष से नहीं मिलता, तो वास्तविक शून्यक नहीं होंगे।
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यदि परवलय (x)-अक्ष को दो अलग-अलग बिंदुओं पर काटता है, तो द्विघात बहुपद के कितने शून्यक होंगे?
If a parabola cuts the (x)-axis at two distinct points, how many zeroes does the quadratic polynomial have?
#quadratic-polynomial
#parabola
#two-zeroes
#x-axis
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A दो / Two
B एक / One
C कोई नहीं / None
D तीन / Three
Explanation opens after your attempt
Step 1
Concept
The graph of a quadratic polynomial is a parabola. Two distinct intersections with the (x)-axis show two real zeroes.
Step 2
Why this answer is correct
The correct answer is A. दो / Two. The graph of a quadratic polynomial is a parabola. Two distinct intersections with the (x)-axis show two real zeroes.
Step 3
Exam Tip
द्विघात बहुपद का ग्राफ परवलय होता है। (x)-अक्ष पर दो अलग-अलग कटाव दो वास्तविक शून्यक बताते हैं।
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यदि परवलय (x)-अक्ष को केवल छूता है, काटता नहीं है, तो द्विघात बहुपद के वास्तविक शून्यकों की संख्या क्या होगी?
If a parabola only touches the (x)-axis and does not cut it, how many real zeroes does the quadratic polynomial have?
#parabola
#touching-x-axis
#one-zero
#quadratic
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A एक / One
B दो / Two
C कोई नहीं / None
D तीन / Three
Explanation opens after your attempt
Step 1
Concept
When a parabola touches the (x)-axis at one point, it has one real zero. In exams, touching the (x)-axis also counts as meeting it.
Step 2
Why this answer is correct
The correct answer is A. एक / One. When a parabola touches the (x)-axis at one point, it has one real zero. In exams, touching the (x)-axis also counts as meeting it.
Step 3
Exam Tip
जब परवलय (x)-अक्ष को केवल एक बिंदु पर छूता है, तो एक वास्तविक शून्यक होता है। परीक्षा में छूना भी (x)-अक्ष से मिलना माना जाता है।
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यदि परवलय पूरा (x)-अक्ष के ऊपर है, तो द्विघात बहुपद के कितने वास्तविक शून्यक होंगे?
If a parabola lies completely above the (x)-axis, how many real zeroes does the quadratic polynomial have?
#quadratic-graph
#no-real-zero
#parabola
#easy
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A कोई नहीं / None
B एक / One
C दो / Two
D अनंत / Infinite
Explanation opens after your attempt
Correct Answer
A. कोई नहीं / None
Step 1
Concept
If the graph does not meet the (x)-axis, no real value satisfies (p(x)=0). Therefore it has (0) real zeroes.
Step 2
Why this answer is correct
The correct answer is A. कोई नहीं / None. If the graph does not meet the (x)-axis, no real value satisfies (p(x)=0). Therefore it has (0) real zeroes.
Step 3
Exam Tip
यदि ग्राफ (x)-अक्ष से नहीं मिलता, तो (p(x)=0) का कोई वास्तविक मान नहीं मिलता। इसलिए वास्तविक शून्यक (0) होंगे।
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किसी बहुपद (p(x)) के शून्यक ज्ञात करने के लिए ग्राफ पर कौन-से बिंदु देखे जाते हैं?
Which points on the graph are observed to find the zeroes of a polynomial (p(x))?
#zeroes
#graph-reading
#x-axis
#polynomials
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A (x)-अक्ष से मिलने वाले बिंदु / Points meeting the (x)-axis
B (y)-अक्ष से मिलने वाले बिंदु / Points meeting the (y)-axis
C ग्राफ के सभी मोड़ / All turns of the graph
D केवल मूल बिंदु / Only the origin
Explanation opens after your attempt
Correct Answer
A. (x)-अक्ष से मिलने वाले बिंदु / Points meeting the (x)-axis
Step 1
Concept
For a zero, (p(x)=0), which means (y=0). Points with (y=0) lie on the (x)-axis.
Step 2
Why this answer is correct
The correct answer is A. (x)-अक्ष से मिलने वाले बिंदु / Points meeting the (x)-axis. For a zero, (p(x)=0), which means (y=0). Points with (y=0) lie on the (x)-axis.
Step 3
Exam Tip
शून्यक के लिए (p(x)=0), यानी (y=0) होना चाहिए। (y=0) वाले बिंदु (x)-अक्ष पर होते हैं।
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यदि ग्राफ (x)-अक्ष को ((0,0)) पर काटता है, तो बहुपद का एक शून्यक क्या होगा?
If a graph cuts the (x)-axis at ((0,0)), what is one zero of the polynomial?
#origin
#zero-of-polynomial
#x-intercept
#easy
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A (0)
B (1)
C (-1)
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Step 1
Concept
The (x)-coordinate of ((0,0)) is (0). Therefore (0) is one zero of the polynomial.
Step 2
Why this answer is correct
The correct answer is A. (0). The (x)-coordinate of ((0,0)) is (0). Therefore (0) is one zero of the polynomial.
Step 3
Exam Tip
बिंदु ((0,0)) का (x)-निर्देशांक (0) है। इसलिए (0) बहुपद का एक शून्यक होगा।
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यदि ग्राफ (x)-अक्ष को (x=-5) पर काटता है, तो कौन-सा कथन सही है?
If a graph cuts the (x)-axis at (x=-5), which statement is correct?
#negative-zero
#x-intercept
#graph
#polynomials
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A (-5) बहुपद का शून्यक है / (-5) is a zero of the polynomial
B (5) बहुपद का शून्यक है / (5) is a zero of the polynomial
C (0) बहुपद का शून्यक है / (0) is a zero of the polynomial
D कोई शून्यक नहीं है / There is no zero
Explanation opens after your attempt
Correct Answer
A. (-5) बहुपद का शून्यक है / (-5) is a zero of the polynomial
Step 1
Concept
The (x)-value where the graph cuts the (x)-axis is the zero. Do not ignore the negative sign.
Step 2
Why this answer is correct
The correct answer is A. (-5) बहुपद का शून्यक है / (-5) is a zero of the polynomial. The (x)-value where the graph cuts the (x)-axis is the zero. Do not ignore the negative sign.
Step 3
Exam Tip
जहाँ ग्राफ (x)-अक्ष को काटता है वही (x)-मान शून्यक होता है। ऋण चिह्न को अनदेखा न करें।
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यदि किसी ग्राफ के (x)-अक्ष से मिलने वाले बिंदु ((1,0)), ((2,0)), और ((5,0)) हैं, तो शून्यकों की संख्या क्या है?
If the points where a graph meets the (x)-axis are ((1,0)), ((2,0)), and ((5,0)), how many zeroes are there?
#number-of-zeroes
#x-intercepts
#graph-reading
#easy
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A (3)
B (2)
C (1)
D (0)
Explanation opens after your attempt
Step 1
Concept
Each distinct intersection with the (x)-axis gives one zero. Here there are three distinct points, so there are three zeroes.
Step 2
Why this answer is correct
The correct answer is A. (3). Each distinct intersection with the (x)-axis gives one zero. Here there are three distinct points, so there are three zeroes.
Step 3
Exam Tip
हर अलग (x)-अक्ष कटाव एक शून्यक देता है। यहाँ तीन अलग बिंदु हैं, इसलिए तीन शून्यक हैं।
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किसी स्थिर अशून्य बहुपद जैसे (p(x)=5) के ग्राफ से शून्यकों के बारे में क्या पता चलता है?
What does the graph of a non-zero constant polynomial like (p(x)=5) show about its zeroes?
#constant-polynomial
#no-zero
#graph
#easy
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A कोई शून्यक नहीं / No zero
B एक शून्यक / One zero
C दो शून्यक / Two zeroes
D अनंत शून्यक / Infinite zeroes
Explanation opens after your attempt
Correct Answer
A. कोई शून्यक नहीं / No zero
Step 1
Concept
The graph of (p(x)=5) is a line parallel to the (x)-axis and does not cut it. Hence it has no zero.
Step 2
Why this answer is correct
The correct answer is A. कोई शून्यक नहीं / No zero. The graph of (p(x)=5) is a line parallel to the (x)-axis and does not cut it. Hence it has no zero.
Step 3
Exam Tip
(p(x)=5) का ग्राफ (x)-अक्ष के समानांतर रेखा है जो (x)-अक्ष को नहीं काटती। इसलिए इसका कोई शून्यक नहीं है।
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यदि (p(x)=x-4) का ग्राफ (x)-अक्ष को काटता है, तो शून्यक क्या होगा?
If the graph of (p(x)=x-4) cuts the (x)-axis, what is the zero?
#linear-polynomial
#zero
#graphical-meaning
#class-10
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A (4)
B (-4)
C (0)
D (1)
Explanation opens after your attempt
Step 1
Concept
For the zero, (x-4=0), so (x=4). The graph also cuts the (x)-axis at (x=4).
Step 2
Why this answer is correct
The correct answer is A. (4). For the zero, (x-4=0), so (x=4). The graph also cuts the (x)-axis at (x=4).
Step 3
Exam Tip
शून्यक के लिए (x-4=0), इसलिए (x=4)। ग्राफ भी (x)-अक्ष को (x=4) पर काटेगा।
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यदि (p(x)=x+2) का ग्राफ (x)-अक्ष को काटता है, तो शून्यक कौन-सा है?
If the graph of (p(x)=x+2) cuts the (x)-axis, which is the zero?
#linear-polynomial
#negative-zero
#x-intercept
#easy
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A (2)
B (-2)
C (0)
D (1)
Explanation opens after your attempt
Step 1
Concept
For the zero, (x+2=0), so (x=-2). The graph cuts the (x)-axis at (x=-2).
Step 2
Why this answer is correct
The correct answer is B. (-2). For the zero, (x+2=0), so (x=-2). The graph cuts the (x)-axis at (x=-2).
Step 3
Exam Tip
शून्यक के लिए (x+2=0), इसलिए (x=-2)। ग्राफ (x)-अक्ष को (x=-2) पर काटेगा।
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ग्राफ पर ((3,0)) बिंदु बहुपद के लिए क्या दर्शाता है?
What does the point ((3,0)) on a polynomial graph represent?
#coordinate-point
#x-axis
#zeroes
#graph
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A (3) बहुपद का शून्यक है / (3) is a zero of the polynomial
B (0) बहुपद का शून्यक है / (0) is a zero of the polynomial
C (3) बहुपद का गुणांक है / (3) is a coefficient of the polynomial
D ग्राफ का अधिकतम मान है / It is the maximum value of the graph
Explanation opens after your attempt
Correct Answer
A. (3) बहुपद का शून्यक है / (3) is a zero of the polynomial
Step 1
Concept
In ((3,0)), (y=0) and (x=3). Therefore (3) is the zero.
Step 2
Why this answer is correct
The correct answer is A. (3) बहुपद का शून्यक है / (3) is a zero of the polynomial. In ((3,0)), (y=0) and (x=3). Therefore (3) is the zero.
Step 3
Exam Tip
((3,0)) में (y=0) है और (x=3) है। इसलिए (3) शून्यक होगा।
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ग्राफ पर ((0,4)) बिंदु मिलने से क्या (0) शून्यक होगा?
Does the point ((0,4)) on a graph mean that (0) is a zero?
#common-mistake
#y-intercept
#zeroes
#graph
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A नहीं, क्योंकि \(y\neq 0\) है / No, because \(y\neq 0\)
B हाँ, क्योंकि (x=0) है / Yes, because (x=0)
C हाँ, क्योंकि बिंदु (y)-अक्ष पर है / Yes, because the point is on the (y)-axis
D निर्धारित नहीं हो सकता / Cannot be determined
Explanation opens after your attempt
Correct Answer
A. नहीं, क्योंकि \(y\neq 0\) है / No, because \(y\neq 0\)
Step 1
Concept
For a zero, (y=0) is required. In ((0,4)), (y=4), so (0) is not a zero.
Step 2
Why this answer is correct
The correct answer is A. नहीं, क्योंकि \(y\neq 0\) है / No, because \(y\neq 0\). For a zero, (y=0) is required. In ((0,4)), (y=4), so (0) is not a zero.
Step 3
Exam Tip
शून्यक के लिए (y=0) होना चाहिए। ((0,4)) में (y=4) है, इसलिए (0) शून्यक नहीं है।
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यदि किसी बहुपद के ग्राफ के (x)-अक्ष से दो कटाव हैं, तो उसके वास्तविक शून्यकों की संख्या क्या होगी?
If a polynomial graph has two intersections with the (x)-axis, how many real zeroes does it have?
#real-zeroes
#x-axis-intersections
#polynomial-graph
#easy
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A दो / Two
B एक / One
C कोई नहीं / None
D चार / Four
Explanation opens after your attempt
Step 1
Concept
Each distinct intersection with the (x)-axis gives one real zero. With two intersections, there are two real zeroes.
Step 2
Why this answer is correct
The correct answer is A. दो / Two. Each distinct intersection with the (x)-axis gives one real zero. With two intersections, there are two real zeroes.
Step 3
Exam Tip
(x)-अक्ष से प्रत्येक अलग कटाव एक वास्तविक शून्यक देता है। दो कटाव होने पर दो वास्तविक शून्यक होंगे।
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किस स्थिति में (x=2) बहुपद (p(x)) का शून्यक कहलाएगा?
In which situation will (x=2) be called a zero of polynomial (p(x))?
#definition
#zero-of-polynomial
#value-test
#easy
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A जब (p(2)=0) हो / When (p(2)=0)
B जब (p(0)=2) हो / When (p(0)=2)
C जब (p(2)=2) हो / When (p(2)=2)
D जब (p(x)=2) हो / When (p(x)=2)
Explanation opens after your attempt
Correct Answer
A. जब (p(2)=0) हो / When (p(2)=0)
Step 1
Concept
A value is called a zero only when the polynomial value at that point is (0). So for (x=2), (p(2)=0) is required.
Step 2
Why this answer is correct
The correct answer is A. जब (p(2)=0) हो / When (p(2)=0). A value is called a zero only when the polynomial value at that point is (0). So for (x=2), (p(2)=0) is required.
Step 3
Exam Tip
किसी मान को शून्यक तभी कहते हैं जब उस पर बहुपद का मान (0) हो। इसलिए (x=2) के लिए (p(2)=0) होना चाहिए।
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यदि (p(-1)=0), तो ग्राफ किस बिंदु से गुजरेगा?
If (p(-1)=0), through which point will the graph pass?
#function-value
#graph-point
#zeroes
#polynomials
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A ((-1,0))
B ((1,0))
C ((0,-1))
D ((0,1))
Explanation opens after your attempt
Correct Answer
A. ((-1,0))
Step 1
Concept
(p(-1)=0) means (y=0) at (x=-1). So the graph passes through ((-1,0)).
Step 2
Why this answer is correct
The correct answer is A. ((-1,0)). (p(-1)=0) means (y=0) at (x=-1). So the graph passes through ((-1,0)).
Step 3
Exam Tip
(p(-1)=0) का अर्थ है (x=-1) पर (y=0)। इसलिए ग्राफ ((-1,0)) से गुजरेगा।
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यदि (p(6)=0), तो बहुपद के ग्राफ का (x)-अक्ष से कौन-सा कटाव होगा?
If (p(6)=0), what will be the (x)-axis intersection of the polynomial graph?
#x-intercept
#function-value
#zeroes
#easy
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A ((6,0))
B ((0,6))
C ((-6,0))
D ((6,6))
Explanation opens after your attempt
Correct Answer
A. ((6,0))
Step 1
Concept
(p(6)=0) means (y=0) when (x=6). Hence the graph cuts the (x)-axis at ((6,0)).
Step 2
Why this answer is correct
The correct answer is A. ((6,0)). (p(6)=0) means (y=0) when (x=6). Hence the graph cuts the (x)-axis at ((6,0)).
Step 3
Exam Tip
(p(6)=0) बताता है कि (x=6) पर (y=0) है। इसलिए ग्राफ (x)-अक्ष को ((6,0)) पर काटता है।
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यदि किसी द्विघात बहुपद का ग्राफ (x)-अक्ष को ((2,0)) और ((7,0)) पर काटता है, तो शून्यक कौन-से हैं?
If the graph of a quadratic polynomial cuts the (x)-axis at ((2,0)) and ((7,0)), what are the zeroes?
#quadratic-polynomial
#x-intercepts
#zeroes
#graph
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A (2) और (7) / (2) and (7)
B (-2) और (-7) / (-2) and (-7)
C (0) और (7) / (0) and (7)
D (2) और (0) / (2) and (0)
Explanation opens after your attempt
Correct Answer
A. (2) और (7) / (2) and (7)
Step 1
Concept
Zeroes are the (x)-coordinates of the points where the graph cuts the (x)-axis. So the zeroes are (2) and (7).
Step 2
Why this answer is correct
The correct answer is A. (2) और (7) / (2) and (7). Zeroes are the (x)-coordinates of the points where the graph cuts the (x)-axis. So the zeroes are (2) and (7).
Step 3
Exam Tip
शून्यक (x)-अक्ष पर कटने वाले बिंदुओं के (x)-निर्देशांक होते हैं। इसलिए शून्यक (2) और (7) हैं।
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यदि किसी परवलय का शीर्ष (x)-अक्ष पर है और वह (x=4) पर है, तो वास्तविक शून्यक क्या होगा?
If the vertex of a parabola lies on the (x)-axis at (x=4), what is the real zero?
#parabola
#vertex
#touching-x-axis
#one-zero
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A (4)
B (0)
C (-4)
D दो शून्यक होंगे / There will be two zeroes
Explanation opens after your attempt
Step 1
Concept
When a parabola touches the (x)-axis at its vertex, it has one real zero. Its (x)-coordinate is (4).
Step 2
Why this answer is correct
The correct answer is A. (4). When a parabola touches the (x)-axis at its vertex, it has one real zero. Its (x)-coordinate is (4).
Step 3
Exam Tip
जब परवलय (x)-अक्ष को शीर्ष पर छूता है, तो एक ही वास्तविक शून्यक होता है। उसका (x)-निर्देशांक (4) है।
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किस ग्राफ से शून्यक (-3) और (2) मिलेंगे?
Which graph will give zeroes (-3) and (2)?
#graph-from-zeroes
#x-intercepts
#polynomials
#easy
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A जो (x)-अक्ष को ((-3,0)) और ((2,0)) पर काटे / One that cuts the (x)-axis at ((-3,0)) and ((2,0))
B जो (y)-अक्ष को ((-3,0)) और ((2,0)) पर काटे / One that cuts the (y)-axis at ((-3,0)) and ((2,0))
C जो (x)-अक्ष को ((0,-3)) और ((0,2)) पर काटे / One that cuts the (x)-axis at ((0,-3)) and ((0,2))
D जो मूल बिंदु से न गुजरे / One that does not pass through origin
Explanation opens after your attempt
Correct Answer
A. जो (x)-अक्ष को ((-3,0)) और ((2,0)) पर काटे / One that cuts the (x)-axis at ((-3,0)) and ((2,0))
Step 1
Concept
If the zeroes are (-3) and (2), the graph cuts the (x)-axis at those (x)-values. So the points are ((-3,0)) and ((2,0)).
Step 2
Why this answer is correct
The correct answer is A. जो (x)-अक्ष को ((-3,0)) और ((2,0)) पर काटे / One that cuts the (x)-axis at ((-3,0)) and ((2,0)). If the zeroes are (-3) and (2), the graph cuts the (x)-axis at those (x)-values. So the points are ((-3,0)) and ((2,0)).
Step 3
Exam Tip
शून्यक (-3) और (2) होने पर ग्राफ (x)-अक्ष को इन्हीं (x)-मानों पर काटेगा। इसलिए बिंदु ((-3,0)) और ((2,0)) होंगे।
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यदि किसी बहुपद का ग्राफ केवल (y)-अक्ष को ((0,3)) पर काटता है और (x)-अक्ष को नहीं काटता, तो वास्तविक शून्यक कितने होंगे?
If a polynomial graph cuts only the (y)-axis at ((0,3)) and does not cut the (x)-axis, how many real zeroes are there?
#y-intercept
#no-real-zero
#common-mistake
#graph
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A (0)
B (1)
C (2)
D (3)
Explanation opens after your attempt
Step 1
Concept
Zeroes are found from intersections with the (x)-axis, not the (y)-axis. So if there is no (x)-axis intersection, there are (0) real zeroes.
Step 2
Why this answer is correct
The correct answer is A. (0). Zeroes are found from intersections with the (x)-axis, not the (y)-axis. So if there is no (x)-axis intersection, there are (0) real zeroes.
Step 3
Exam Tip
शून्यक (x)-अक्ष से मिलने पर मिलते हैं, (y)-अक्ष से नहीं। इसलिए (x)-अक्ष से कटाव न होने पर वास्तविक शून्यक (0) होंगे।
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बहुपद (p(x)) के ग्राफ में (y=p(x)) होता है। शून्यक पर (y) का मान क्या होगा?
In the graph of polynomial (p(x)), (y=p(x)). What is the value of (y) at a zero?
#definition
#y-value
#zeroes
#graph
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A (0)
B (1)
C (-1)
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Step 1
Concept
At a zero, the value of the polynomial is (0). Therefore the (y)-value at that point on the graph is (0).
Step 2
Why this answer is correct
The correct answer is A. (0). At a zero, the value of the polynomial is (0). Therefore the (y)-value at that point on the graph is (0).
Step 3
Exam Tip
शून्यक पर बहुपद का मान (0) होता है। इसलिए ग्राफ पर उस बिंदु का (y)-मान (0) होगा।
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यदि रेखा (y=2x-6) (x)-अक्ष को काटती है, तो संबंधित रैखिक बहुपद का शून्यक क्या है?
If the line (y=2x-6) cuts the (x)-axis, what is the zero of the related linear polynomial?
#linear-graph
#x-intercept
#zero
#polynomial
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A (3)
B (-3)
C (6)
D (-6)
Explanation opens after your attempt
Step 1
Concept
On the (x)-axis, (y=0), so (2x-6=0) gives (x=3). This is the graphical zero.
Step 2
Why this answer is correct
The correct answer is A. (3). On the (x)-axis, (y=0), so (2x-6=0) gives (x=3). This is the graphical zero.
Step 3
Exam Tip
(x)-अक्ष पर (y=0), इसलिए (2x-6=0) से (x=3) मिलता है। यही ग्राफीय शून्यक है।
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यदि रेखा (y=x+7) का ग्राफ (x)-अक्ष को काटता है, तो शून्यक क्या होगा?
If the graph of the line (y=x+7) cuts the (x)-axis, what is the zero?
#linear-polynomial
#zero
#x-intercept
#easy
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A (7)
B (-7)
C (0)
D (1)
Explanation opens after your attempt
Step 1
Concept
On the (x)-axis, (y=0), so (x+7=0) gives (x=-7). Watch the negative sign carefully.
Step 2
Why this answer is correct
The correct answer is B. (-7). On the (x)-axis, (y=0), so (x+7=0) gives (x=-7). Watch the negative sign carefully.
Step 3
Exam Tip
(x)-अक्ष पर (y=0), इसलिए (x+7=0) से (x=-7) मिलता है। ऋण चिह्न को ध्यान से देखें।
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यदि किसी बहुपद का ग्राफ (x)-अक्ष को ((5,0)) पर केवल छूता है, तो कौन-सा कथन सही है?
If the graph of a polynomial only touches the (x)-axis at ((5,0)), which statement is correct?
#touching-x-axis
#zeroes
#graphical-meaning
#easy
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A (5) शून्यक है / (5) is a zero
B (0) शून्यक है / (0) is a zero
C कोई शून्यक नहीं है / There is no zero
D (-5) शून्यक है / (-5) is a zero
Explanation opens after your attempt
Correct Answer
A. (5) शून्यक है / (5) is a zero
Step 1
Concept
Touching the (x)-axis also shows (p(x)=0). Therefore (x=5) is a zero.
Step 2
Why this answer is correct
The correct answer is A. (5) शून्यक है / (5) is a zero. Touching the (x)-axis also shows (p(x)=0). Therefore (x=5) is a zero.
Step 3
Exam Tip
ग्राफ का (x)-अक्ष को छूना भी (p(x)=0) को दिखाता है। इसलिए (x=5) शून्यक है।
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यदि बहुपद के ग्राफ में (x)-अक्ष से कटाव की संख्या (4) है, तो वास्तविक शून्यकों की संख्या क्या होगी?
If the number of intersections of a polynomial graph with the (x)-axis is (4), how many real zeroes are there?
#number-of-zeroes
#x-axis
#graph-reading
#polynomials
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A (4)
B (3)
C (2)
D (0)
Explanation opens after your attempt
Step 1
Concept
Each distinct (x)-axis intersection represents one real zero. Therefore (4) intersections give (4) real zeroes.
Step 2
Why this answer is correct
The correct answer is A. (4). Each distinct (x)-axis intersection represents one real zero. Therefore (4) intersections give (4) real zeroes.
Step 3
Exam Tip
प्रत्येक अलग (x)-अक्ष कटाव एक वास्तविक शून्यक बताता है। इसलिए (4) कटावों से (4) वास्तविक शून्यक मिलेंगे।
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यदि (p(2)=5), तो क्या (2) बहुपद का शून्यक है?
If (p(2)=5), is (2) a zero of the polynomial?
#value-test
#not-zero
#polynomials
#easy
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A नहीं / No
B हाँ / Yes
C केवल द्विघात में / Only in quadratic
D केवल रैखिक में / Only in linear
Explanation opens after your attempt
Correct Answer
A. नहीं / No
Step 1
Concept
For (2) to be a zero, (p(2)=0) must hold. Here (p(2)=5), so (2) is not a zero.
Step 2
Why this answer is correct
The correct answer is A. नहीं / No. For (2) to be a zero, (p(2)=0) must hold. Here (p(2)=5), so (2) is not a zero.
Step 3
Exam Tip
शून्यक होने के लिए (p(2)=0) होना चाहिए। यहाँ (p(2)=5), इसलिए (2) शून्यक नहीं है।
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यदि (p(a)=0), तो ग्राफ किस बिंदु से अवश्य गुजरेगा?
If (p(a)=0), through which point must the graph pass?
#general-zero
#coordinate
#graph
#polynomials
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A ((a,0))
B ((0,a))
C ((a,a))
D ((-a,0))
Explanation opens after your attempt
Correct Answer
A. ((a,0))
Step 1
Concept
(p(a)=0) means (y=0) at (x=a). Therefore the graph passes through ((a,0)).
Step 2
Why this answer is correct
The correct answer is A. ((a,0)). (p(a)=0) means (y=0) at (x=a). Therefore the graph passes through ((a,0)).
Step 3
Exam Tip
(p(a)=0) का अर्थ है (x=a) पर (y=0)। इसलिए ग्राफ ((a,0)) से गुजरेगा।
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यदि ग्राफ (x)-अक्ष को (x=1), (x=3), और (x=6) पर काटता है, तो शून्यक कौन-से हैं?
If a graph cuts the (x)-axis at (x=1), (x=3), and (x=6), what are the zeroes?
#x-values
#zeroes
#graph-reading
#easy
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A (1), (3), (6)
B (0), (3), (6)
C (1), (0), (6)
D (-1), (-3), (-6)
Explanation opens after your attempt
Correct Answer
A. (1), (3), (6)
Step 1
Concept
Zeroes are the (x)-values where the graph cuts the (x)-axis. So the zeroes are (1), (3), and (6).
Step 2
Why this answer is correct
The correct answer is A. (1), (3), (6). Zeroes are the (x)-values where the graph cuts the (x)-axis. So the zeroes are (1), (3), and (6).
Step 3
Exam Tip
शून्यक वही (x)-मान होते हैं जहाँ ग्राफ (x)-अक्ष को काटता है। इसलिए शून्यक (1), (3), और (6) हैं।
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यदि परवलय (x)-अक्ष को ((-1,0)) और ((5,0)) पर काटता है, तो वास्तविक शून्यकों की संख्या क्या है?
If a parabola cuts the (x)-axis at ((-1,0)) and ((5,0)), how many real zeroes are there?
#parabola
#two-zeroes
#x-intercepts
#easy
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A दो / Two
B एक / One
C कोई नहीं / None
D तीन / Three
Explanation opens after your attempt
Step 1
Concept
Two distinct (x)-axis intersections show two real zeroes. Here the zeroes are (-1) and (5).
Step 2
Why this answer is correct
The correct answer is A. दो / Two. Two distinct (x)-axis intersections show two real zeroes. Here the zeroes are (-1) and (5).
Step 3
Exam Tip
दो अलग-अलग (x)-अक्ष कटाव दो वास्तविक शून्यक बताते हैं। यहाँ शून्यक (-1) और (5) हैं।
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यदि परवलय (x)-अक्ष को ((2,0)) पर छूकर ऊपर लौट जाता है, तो शून्यकों की संख्या क्या होगी?
If a parabola touches the (x)-axis at ((2,0)) and turns upward, how many zeroes does it have?
#touching-parabola
#one-zero
#quadratic
#easy
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A एक / One
B दो / Two
C कोई नहीं / None
D अनंत / Infinite
Explanation opens after your attempt
Step 1
Concept
The parabola meets the (x)-axis at only one point. Therefore it has one real zero, (2).
Step 2
Why this answer is correct
The correct answer is A. एक / One. The parabola meets the (x)-axis at only one point. Therefore it has one real zero, (2).
Step 3
Exam Tip
परवलय (x)-अक्ष से केवल एक बिंदु पर मिलता है। इसलिए उसका एक वास्तविक शून्यक (2) होगा।
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किस स्थिति में द्विघात बहुपद के दो वास्तविक शून्यक होंगे?
In which case will a quadratic polynomial have two real zeroes?
#quadratic-zeroes
#parabola
#x-axis
#concept
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A जब उसका ग्राफ (x)-अक्ष को दो अलग बिंदुओं पर काटे / When its graph cuts the (x)-axis at two distinct points
B जब उसका ग्राफ (y)-अक्ष को एक बार काटे / When its graph cuts the (y)-axis once
C जब उसका ग्राफ (x)-अक्ष को न काटे / When its graph does not cut the (x)-axis
D जब उसका ग्राफ केवल ऊपर हो / When its graph is only above
Explanation opens after your attempt
Correct Answer
A. जब उसका ग्राफ (x)-अक्ष को दो अलग बिंदुओं पर काटे / When its graph cuts the (x)-axis at two distinct points
Step 1
Concept
Real zeroes of a quadratic polynomial are found from points where it meets the (x)-axis. Two distinct intersections give two real zeroes.
Step 2
Why this answer is correct
The correct answer is A. जब उसका ग्राफ (x)-अक्ष को दो अलग बिंदुओं पर काटे / When its graph cuts the (x)-axis at two distinct points. Real zeroes of a quadratic polynomial are found from points where it meets the (x)-axis. Two distinct intersections give two real zeroes.
Step 3
Exam Tip
द्विघात बहुपद के वास्तविक शून्यक (x)-अक्ष से मिलने वाले बिंदुओं से मिलते हैं। दो अलग कटाव दो वास्तविक शून्यक देते हैं।
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किस स्थिति में द्विघात बहुपद का कोई वास्तविक शून्यक नहीं होगा?
In which case will a quadratic polynomial have no real zero?
#no-real-zero
#quadratic-graph
#parabola
#easy
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A जब उसका ग्राफ (x)-अक्ष को न छुए और न काटे / When its graph neither touches nor cuts the (x)-axis
B जब उसका ग्राफ (x)-अक्ष को दो बार काटे / When its graph cuts the (x)-axis twice
C जब उसका ग्राफ (x)-अक्ष को एक बार छुए / When its graph touches the (x)-axis once
D जब उसका ग्राफ मूल बिंदु से गुजरे / When its graph passes through origin
Explanation opens after your attempt
Correct Answer
A. जब उसका ग्राफ (x)-अक्ष को न छुए और न काटे / When its graph neither touches nor cuts the (x)-axis
Step 1
Concept
For real zeroes, the graph must meet the (x)-axis. If it does not meet the (x)-axis, there is no real zero.
Step 2
Why this answer is correct
The correct answer is A. जब उसका ग्राफ (x)-अक्ष को न छुए और न काटे / When its graph neither touches nor cuts the (x)-axis. For real zeroes, the graph must meet the (x)-axis. If it does not meet the (x)-axis, there is no real zero.
Step 3
Exam Tip
वास्तविक शून्यक के लिए ग्राफ का (x)-अक्ष से मिलना जरूरी है। यदि ग्राफ (x)-अक्ष से नहीं मिलता, तो कोई वास्तविक शून्यक नहीं होगा।
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किसी बहुपद के ग्राफ में (x)-अक्ष से कटावों की संख्या क्या बताती है?
What does the number of intersections with the (x)-axis tell in a polynomial graph?
#graph-reading
#number-of-zeroes
#x-axis
#concept
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A वास्तविक शून्यकों की संख्या / Number of real zeroes
B गुणांकों की संख्या / Number of coefficients
C घातांक का मान हमेशा / Always the degree
D (y)-अक्ष का कटाव / (y)-intercept
Explanation opens after your attempt
Correct Answer
A. वास्तविक शून्यकों की संख्या / Number of real zeroes
Step 1
Concept
The number of distinct times the graph meets the (x)-axis gives the number of real zeroes. Check this first while reading a graph.
Step 2
Why this answer is correct
The correct answer is A. वास्तविक शून्यकों की संख्या / Number of real zeroes. The number of distinct times the graph meets the (x)-axis gives the number of real zeroes. Check this first while reading a graph.
Step 3
Exam Tip
ग्राफ जितनी बार (x)-अक्ष से अलग-अलग मिलता है, उतने वास्तविक शून्यक होते हैं। इसे ग्राफ पढ़ते समय सबसे पहले देखें।
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यदि ग्राफ (x)-अक्ष को ((-4,0)) पर काटता है, तो कौन-सा मान बहुपद को शून्य बनाता है?
If a graph cuts the (x)-axis at ((-4,0)), which value makes the polynomial zero?
#negative-x-intercept
#zeroes
#graph
#easy
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A (-4)
B (4)
C (0)
D (1)
Explanation opens after your attempt
Step 1
Concept
The (x)-coordinate of the intersection point is (-4). Therefore the polynomial value is (0) at (x=-4).
Step 2
Why this answer is correct
The correct answer is A. (-4). The (x)-coordinate of the intersection point is (-4). Therefore the polynomial value is (0) at (x=-4).
Step 3
Exam Tip
कटाव बिंदु का (x)-निर्देशांक (-4) है। इसलिए (x=-4) पर बहुपद का मान (0) होगा।
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यदि (p(0)=0), तो ग्राफ किस विशेष बिंदु से गुजरेगा?
If (p(0)=0), through which special point will the graph pass?
#origin
#zero
#p-of-zero
#graph
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A मूल बिंदु / Origin
B केवल ((1,0)) / Only ((1,0))
C केवल ((0,1)) / Only ((0,1))
D ((-1,0))
Explanation opens after your attempt
Correct Answer
A. मूल बिंदु / Origin
Step 1
Concept
(p(0)=0) means (y=0) at (x=0). So the graph passes through the origin ((0,0)).
Step 2
Why this answer is correct
The correct answer is A. मूल बिंदु / Origin. (p(0)=0) means (y=0) at (x=0). So the graph passes through the origin ((0,0)).
Step 3
Exam Tip
(p(0)=0) का अर्थ है (x=0) पर (y=0)। इसलिए ग्राफ मूल बिंदु ((0,0)) से गुजरेगा।
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किस बहुपद का ग्राफ (x)-अक्ष को (x=0) पर काटेगा?
Which polynomial graph will cut the (x)-axis at (x=0)?
#condition-for-zero
#origin
#x-axis
#polynomial
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A जिसके लिए (p(0)=0) / One for which (p(0)=0)
B जिसके लिए (p(0)=5) / One for which (p(0)=5)
C जिसके लिए (p(1)=0) / One for which (p(1)=0)
D जिसके लिए (p(-1)=1) / One for which (p(-1)=1)
Explanation opens after your attempt
Correct Answer
A. जिसके लिए (p(0)=0) / One for which (p(0)=0)
Step 1
Concept
To cut the (x)-axis at (x=0), the (y)-value must be (0). Hence (p(0)=0) is required.
Step 2
Why this answer is correct
The correct answer is A. जिसके लिए (p(0)=0) / One for which (p(0)=0). To cut the (x)-axis at (x=0), the (y)-value must be (0). Hence (p(0)=0) is required.
Step 3
Exam Tip
(x=0) पर (x)-अक्ष से कटने के लिए (y=0) होना चाहिए। इसलिए (p(0)=0) होना जरूरी है।
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यदि बहुपद का ग्राफ (x)-अक्ष को ((a,0)) पर काटता है, तो शून्यक क्या होगा?
If the graph of a polynomial cuts the (x)-axis at ((a,0)), what is the zero?
#general-coordinate
#zeroes
#x-intercept
#easy
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A (a)
B (0)
C (-a)
D \(a^2\)
Explanation opens after your attempt
Step 1
Concept
The zero is the (x)-coordinate of the intersection point. In ((a,0)), the (x)-coordinate is (a).
Step 2
Why this answer is correct
The correct answer is A. (a). The zero is the (x)-coordinate of the intersection point. In ((a,0)), the (x)-coordinate is (a).
Step 3
Exam Tip
शून्यक कटाव बिंदु का (x)-निर्देशांक होता है। ((a,0)) में (x)-निर्देशांक (a) है।
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बहुपद के शून्यकों को ग्राफ में किस नाम से भी समझा जा सकता है?
By what name can the zeroes of a polynomial also be understood on a graph?
#x-intercepts
#zeroes
#terminology
#graph
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A (x)-अवरोध / (x)-intercepts
B (y)-अवरोध / (y)-intercepts
C ढाल / Slope
D शीर्ष / Vertex
Explanation opens after your attempt
Correct Answer
A. (x)-अवरोध / (x)-intercepts
Step 1
Concept
Zeroes are the (x)-values where the graph cuts or touches the (x)-axis. Hence they are linked with (x)-intercepts.
Step 2
Why this answer is correct
The correct answer is A. (x)-अवरोध / (x)-intercepts. Zeroes are the (x)-values where the graph cuts or touches the (x)-axis. Hence they are linked with (x)-intercepts.
Step 3
Exam Tip
शून्यक वही (x)-मान हैं जहाँ ग्राफ (x)-अक्ष को काटता या छूता है। इसलिए इन्हें (x)-अवरोध से जोड़ा जाता है।
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यदि किसी बहुपद का ग्राफ (x)-अक्ष को एक बार काटता और एक बार छूता है, तो अलग-अलग वास्तविक शून्यकों की संख्या क्या होगी?
If a polynomial graph cuts the (x)-axis once and touches it once, how many distinct real zeroes will it have?
#distinct-zeroes
#touching-cutting
#x-axis
#polynomials
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A दो / Two
B एक / One
C तीन / Three
D कोई नहीं / None
Explanation opens after your attempt
Step 1
Concept
Both cutting and touching count as meeting the (x)-axis. If the two points are distinct, there are two distinct real zeroes.
Step 2
Why this answer is correct
The correct answer is A. दो / Two. Both cutting and touching count as meeting the (x)-axis. If the two points are distinct, there are two distinct real zeroes.
Step 3
Exam Tip
कटना और छूना दोनों (x)-अक्ष से मिलना है। यदि दोनों बिंदु अलग हैं, तो दो अलग वास्तविक शून्यक होंगे।
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यदि ग्राफ (x)-अक्ष को ((8,0)) पर काटता है, तो (p(8)) का मान क्या होगा?
If the graph cuts the (x)-axis at ((8,0)), what is the value of (p(8))?
#function-value
#x-axis
#zeroes
#easy
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A (0)
B (8)
C (-8)
D (1)
Explanation opens after your attempt
Step 1
Concept
On the (x)-axis, (y=0). Therefore at ((8,0)), (p(8)=0).
Step 2
Why this answer is correct
The correct answer is A. (0). On the (x)-axis, (y=0). Therefore at ((8,0)), (p(8)=0).
Step 3
Exam Tip
(x)-अक्ष पर (y=0) होता है। इसलिए ((8,0)) पर (p(8)=0) होगा।
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यदि (p(-6)=0), तो कौन-सा बिंदु ग्राफ पर होगा?
If (p(-6)=0), which point will lie on the graph?
#graph-point
#function-value
#negative-zero
#easy
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A ((-6,0))
B ((6,0))
C ((0,-6))
D ((0,6))
Explanation opens after your attempt
Correct Answer
A. ((-6,0))
Step 1
Concept
(p(-6)=0) means (y=0) at (x=-6). So the point ((-6,0)) lies on the graph.
Step 2
Why this answer is correct
The correct answer is A. ((-6,0)). (p(-6)=0) means (y=0) at (x=-6). So the point ((-6,0)) lies on the graph.
Step 3
Exam Tip
(p(-6)=0) बताता है कि (x=-6) पर (y=0) है। इसलिए बिंदु ((-6,0)) ग्राफ पर होगा।
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यदि किसी ग्राफ का (x)-अक्ष से कोई साझा बिंदु नहीं है, तो शून्यकों के बारे में क्या निष्कर्ष है?
If a graph has no common point with the (x)-axis, what is the conclusion about its zeroes?
#no-common-point
#no-real-zero
#graph
#polynomials
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A कोई वास्तविक शून्यक नहीं / No real zero
B एक वास्तविक शून्यक / One real zero
C दो वास्तविक शून्यक / Two real zeroes
D अनंत वास्तविक शून्यक / Infinite real zeroes
Explanation opens after your attempt
Correct Answer
A. कोई वास्तविक शून्यक नहीं / No real zero
Step 1
Concept
Real zeroes are obtained from common points of the graph and the (x)-axis. If there is no common point, there is no real zero.
Step 2
Why this answer is correct
The correct answer is A. कोई वास्तविक शून्यक नहीं / No real zero. Real zeroes are obtained from common points of the graph and the (x)-axis. If there is no common point, there is no real zero.
Step 3
Exam Tip
वास्तविक शून्यक ग्राफ और (x)-अक्ष के साझा बिंदुओं से मिलते हैं। साझा बिंदु न हो तो वास्तविक शून्यक नहीं होगा।
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एक बहुपद का ग्राफ (x)-अक्ष को केवल ((-2,0)) पर छूता है। अलग वास्तविक शून्यक कौन-सा है?
A polynomial graph only touches the (x)-axis at ((-2,0)). What is the distinct real zero?
#touching-point
#distinct-zero
#graph
#easy
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A (-2)
B (2)
C (0)
D कोई नहीं / None
Explanation opens after your attempt
Step 1
Concept
A touching point also gives (p(x)=0). Therefore the distinct real zero is (-2).
Step 2
Why this answer is correct
The correct answer is A. (-2). A touching point also gives (p(x)=0). Therefore the distinct real zero is (-2).
Step 3
Exam Tip
छूने वाला बिंदु भी (p(x)=0) देता है। इसलिए अलग वास्तविक शून्यक (-2) है।
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यदि ग्राफ (x)-अक्ष को ((r,0)) और ((s,0)) पर काटता है, जहाँ \(r\neq s\), तो शून्यक क्या होंगे?
If a graph cuts the (x)-axis at ((r,0)) and ((s,0)), where \(r\neq s\), what are the zeroes?
#general-zeroes
#x-intercepts
#polynomial-graph
#easy
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A (r) और (s) / (r) and (s)
B (0) और (0) / (0) and (0)
C (-r) और (-s) / (-r) and (-s)
D (r+s) और (rs) / (r+s) and (rs)
Explanation opens after your attempt
Correct Answer
A. (r) और (s) / (r) and (s)
Step 1
Concept
Zeroes are the (x)-coordinates of the points where the graph cuts the (x)-axis. Hence the zeroes are (r) and (s).
Step 2
Why this answer is correct
The correct answer is A. (r) और (s) / (r) and (s). Zeroes are the (x)-coordinates of the points where the graph cuts the (x)-axis. Hence the zeroes are (r) and (s).
Step 3
Exam Tip
शून्यक (x)-अक्ष के कटाव बिंदुओं के (x)-निर्देशांक होते हैं। इसलिए शून्यक (r) और (s) हैं।
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किसी बहुपद के ग्राफ पर शून्यक पहचानने के लिए कौन-सा मान शून्य होना चाहिए?
Which value must be zero to identify a zero on the graph of a polynomial?
#polynomials
#zeroes
#graph
#value-test
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A बहुपद का मान / Value of the polynomial
B चर का गुणांक / Coefficient of the variable
C घात का मान / Value of the degree
D स्थिर पद / Constant term
Explanation opens after your attempt
Correct Answer
A. बहुपद का मान / Value of the polynomial
Step 1
Concept
At a zero, the polynomial value is (0). While reading a graph, look for points where (y=0).
Step 2
Why this answer is correct
The correct answer is A. बहुपद का मान / Value of the polynomial. At a zero, the polynomial value is (0). While reading a graph, look for points where (y=0).
Step 3
Exam Tip
शून्यक पर बहुपद का मान (0) होता है। ग्राफ पढ़ते समय (y=0) वाले बिंदु देखें।
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यदि ग्राफ (x)-अक्ष को ((-4,0)) और ((1,0)) पर काटता है, तो शून्यक कौन-से हैं?
If a graph cuts the (x)-axis at ((-4,0)) and ((1,0)), what are the zeroes?
#x-intercepts
#zeroes
#graph-reading
#polynomials
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A (-4) और (1) / (-4) and (1)
B (4) और (-1) / (4) and (-1)
C (-4) और (0) / (-4) and (0)
D (0) और (1) / (0) and (1)
Explanation opens after your attempt
Correct Answer
A. (-4) और (1) / (-4) and (1)
Step 1
Concept
Zeroes are the (x)-coordinates of the points where the graph cuts the (x)-axis. Hence the zeroes are (-4) and (1).
Step 2
Why this answer is correct
The correct answer is A. (-4) और (1) / (-4) and (1). Zeroes are the (x)-coordinates of the points where the graph cuts the (x)-axis. Hence the zeroes are (-4) and (1).
Step 3
Exam Tip
शून्यक (x)-अक्ष पर कटने वाले बिंदुओं के (x)-निर्देशांक होते हैं। इसलिए शून्यक (-4) और (1) हैं।
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यदि किसी बहुपद के ग्राफ का (x)-अक्ष से केवल एक साझा बिंदु ((6,0)) है, तो अलग वास्तविक शून्यक क्या होगा?
If a polynomial graph has only one common point with the (x)-axis at ((6,0)), what is the distinct real zero?
#distinct-zero
#x-axis
#graph
#easy
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A (6)
B (-6)
C (0)
D कोई नहीं / None
Explanation opens after your attempt
Step 1
Concept
The common point ((6,0)) has (x)-coordinate (6). So the distinct real zero is (6).
Step 2
Why this answer is correct
The correct answer is A. (6). The common point ((6,0)) has (x)-coordinate (6). So the distinct real zero is (6).
Step 3
Exam Tip
एक साझा बिंदु ((6,0)) का (x)-निर्देशांक (6) है। इसलिए अलग वास्तविक शून्यक (6) होगा।
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यदि (p(9)=0), तो ग्राफ किस बिंदु से गुजरेगा?
If (p(9)=0), through which point will the graph pass?
#function-value
#graph-point
#zeroes
#class-10
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A ((9,0))
B ((0,9))
C ((-9,0))
D ((9,9))
Explanation opens after your attempt
Correct Answer
A. ((9,0))
Step 1
Concept
(p(9)=0) means (y=0) when (x=9). Therefore the graph passes through ((9,0)).
Step 2
Why this answer is correct
The correct answer is A. ((9,0)). (p(9)=0) means (y=0) when (x=9). Therefore the graph passes through ((9,0)).
Step 3
Exam Tip
(p(9)=0) का अर्थ है (x=9) पर (y=0)। इसलिए ग्राफ ((9,0)) से गुजरेगा।
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यदि (p(-3)=0), तो बहुपद का कौन-सा शून्यक है?
If (p(-3)=0), which value is a zero of the polynomial?
#zero-definition
#function-value
#negative-zero
#easy
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A (-3)
B (3)
C (0)
D (1)
Explanation opens after your attempt
Step 1
Concept
The (x)-value for which (p(x)=0) is a zero. Hence (-3) is a zero of the polynomial.
Step 2
Why this answer is correct
The correct answer is A. (-3). The (x)-value for which (p(x)=0) is a zero. Hence (-3) is a zero of the polynomial.
Step 3
Exam Tip
जिस (x)-मान पर (p(x)=0) हो वही शून्यक होता है। इसलिए (-3) बहुपद का शून्यक है।
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किसी ग्राफ का (y)-अक्ष से कटना शून्यक क्यों नहीं बताता?
Why does the intersection of a graph with the (y)-axis not directly give a zero?
#common-mistake
#y-intercept
#x-intercept
#zeroes
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A क्योंकि शून्यक के लिए (y=0) चाहिए / Because a zero needs (y=0)
B क्योंकि शून्यक के लिए (x=0) चाहिए / Because a zero needs (x=0)
C क्योंकि हर बिंदु शून्यक होता है / Because every point is a zero
D क्योंकि (y)-अक्ष पर ग्राफ नहीं बनता / Because graphs are not drawn on the (y)-axis
Explanation opens after your attempt
Correct Answer
A. क्योंकि शून्यक के लिए (y=0) चाहिए / Because a zero needs (y=0)
Step 1
Concept
Zeroes are linked to the (x)-axis where (y=0). A (y)-axis intersection only shows the value of the polynomial at (x=0).
Step 2
Why this answer is correct
The correct answer is A. क्योंकि शून्यक के लिए (y=0) चाहिए / Because a zero needs (y=0). Zeroes are linked to the (x)-axis where (y=0). A (y)-axis intersection only shows the value of the polynomial at (x=0).
Step 3
Exam Tip
शून्यक (x)-अक्ष से जुड़े होते हैं जहाँ (y=0) होता है। (y)-अक्ष से कटाव केवल (x=0) पर बहुपद का मान बताता है।
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यदि ग्राफ (x)-अक्ष को तीन अलग-अलग बिंदुओं पर काटता है, तो वास्तविक शून्यकों की संख्या क्या होगी?
If a graph cuts the (x)-axis at three distinct points, how many real zeroes will it have?
#real-zeroes
#x-axis
#graph-reading
#easy
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A तीन / Three
B दो / Two
C एक / One
D कोई नहीं / None
Explanation opens after your attempt
Correct Answer
A. तीन / Three
Step 1
Concept
Each distinct intersection with the (x)-axis gives one real zero. Therefore three distinct intersections give three real zeroes.
Step 2
Why this answer is correct
The correct answer is A. तीन / Three. Each distinct intersection with the (x)-axis gives one real zero. Therefore three distinct intersections give three real zeroes.
Step 3
Exam Tip
हर अलग (x)-अक्ष कटाव एक वास्तविक शून्यक देता है। इसलिए तीन अलग कटावों से तीन वास्तविक शून्यक मिलेंगे।
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यदि किसी परवलय का (x)-अक्ष से कोई साझा बिंदु नहीं है, तो द्विघात बहुपद के वास्तविक शून्यक कितने होंगे?
If a parabola has no common point with the (x)-axis, how many real zeroes does the quadratic polynomial have?
#quadratic-polynomial
#parabola
#no-real-zero
#graph
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A (0)
B (1)
C (2)
D (3)
Explanation opens after your attempt
Step 1
Concept
Real zeroes are found only when the graph meets the (x)-axis. With no common point, there are (0) real zeroes.
Step 2
Why this answer is correct
The correct answer is A. (0). Real zeroes are found only when the graph meets the (x)-axis. With no common point, there are (0) real zeroes.
Step 3
Exam Tip
वास्तविक शून्यक तभी मिलते हैं जब ग्राफ (x)-अक्ष से मिले। साझा बिंदु न होने पर वास्तविक शून्यक (0) होंगे।
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यदि परवलय (x)-अक्ष को ((3,0)) पर केवल छूता है, तो द्विघात बहुपद के वास्तविक शून्यकों की संख्या क्या है?
If a parabola only touches the (x)-axis at ((3,0)), how many real zeroes does the quadratic polynomial have?
#touching-x-axis
#one-zero
#parabola
#easy
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A एक / One
B दो / Two
C कोई नहीं / None
D चार / Four
Explanation opens after your attempt
Step 1
Concept
Touching also means meeting the (x)-axis, but there is only one point. Hence there is one real zero.
Step 2
Why this answer is correct
The correct answer is A. एक / One. Touching also means meeting the (x)-axis, but there is only one point. Hence there is one real zero.
Step 3
Exam Tip
छूना भी (x)-अक्ष से मिलना है, लेकिन बिंदु केवल एक है। इसलिए एक वास्तविक शून्यक होगा।
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यदि परवलय (x)-अक्ष को ((-5,0)) और ((2,0)) पर काटता है, तो शून्यक कौन-से होंगे?
If a parabola cuts the (x)-axis at ((-5,0)) and ((2,0)), what will be the zeroes?
#parabola
#two-zeroes
#x-intercepts
#easy
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A (-5) और (2) / (-5) and (2)
B (5) और (-2) / (5) and (-2)
C (-5) और (0) / (-5) and (0)
D (0) और (2) / (0) and (2)
Explanation opens after your attempt
Correct Answer
A. (-5) और (2) / (-5) and (2)
Step 1
Concept
Zeroes are the (x)-coordinates of the intersection points. Hence the zeroes are (-5) and (2).
Step 2
Why this answer is correct
The correct answer is A. (-5) और (2) / (-5) and (2). Zeroes are the (x)-coordinates of the intersection points. Hence the zeroes are (-5) and (2).
Step 3
Exam Tip
शून्यक कटाव बिंदुओं के (x)-निर्देशांक होते हैं। इसलिए शून्यक (-5) और (2) हैं।
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ग्राफ में (x)-अक्ष से कटाव बिंदु ((a,0)) हो, तो (p(a)) का मान क्या होगा?
If ((a,0)) is an intersection point with the (x)-axis on the graph, what is the value of (p(a))?
#general-point
#p-of-a
#zeroes
#x-axis
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A (0)
B (a)
C (-a)
D (1)
Explanation opens after your attempt
Step 1
Concept
On the (x)-axis, (y=0). Therefore at ((a,0)), (p(a)=0).
Step 2
Why this answer is correct
The correct answer is A. (0). On the (x)-axis, (y=0). Therefore at ((a,0)), (p(a)=0).
Step 3
Exam Tip
(x)-अक्ष पर (y=0) होता है। इसलिए ((a,0)) पर (p(a)=0) होगा।
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यदि (p(0)=4), तो क्या (0) बहुपद का शून्यक है?
If (p(0)=4), is (0) a zero of the polynomial?
#value-test
#not-zero
#origin
#polynomials
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A नहीं / No
B हाँ / Yes
C केवल रैखिक बहुपद में / Only in a linear polynomial
D केवल द्विघात बहुपद में / Only in a quadratic polynomial
Explanation opens after your attempt
Correct Answer
A. नहीं / No
Step 1
Concept
For (0) to be a zero, (p(0)=0) must be true. Here (p(0)=4), so (0) is not a zero.
Step 2
Why this answer is correct
The correct answer is A. नहीं / No. For (0) to be a zero, (p(0)=0) must be true. Here (p(0)=4), so (0) is not a zero.
Step 3
Exam Tip
शून्यक होने के लिए (p(0)=0) होना चाहिए। यहाँ (p(0)=4), इसलिए (0) शून्यक नहीं है।
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रेखा (y=3x-12) का (x)-अक्ष से कटाव किस (x)-मान पर होगा?
At which (x)-value will the line (y=3x-12) cut the (x)-axis?
#linear-polynomial
#x-intercept
#zero
#easy
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A (4)
B (-4)
C (12)
D (3)
Explanation opens after your attempt
Step 1
Concept
On the (x)-axis, (y=0), so (3x-12=0) gives (x=4). This is the zero.
Step 2
Why this answer is correct
The correct answer is A. (4). On the (x)-axis, (y=0), so (3x-12=0) gives (x=4). This is the zero.
Step 3
Exam Tip
(x)-अक्ष पर (y=0), इसलिए (3x-12=0) से (x=4) मिलता है। यही शून्यक है।
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रेखा (y=x-8) का शून्यक कौन-सा है?
What is the zero of the line (y=x-8)?
#linear-graph
#zero
#x-axis
#easy
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A (8)
B (-8)
C (0)
D (1)
Explanation opens after your attempt
Step 1
Concept
For the zero, (y=0), so (x-8=0) gives (x=8). The graph cuts the (x)-axis at (8).
Step 2
Why this answer is correct
The correct answer is A. (8). For the zero, (y=0), so (x-8=0) gives (x=8). The graph cuts the (x)-axis at (8).
Step 3
Exam Tip
शून्यक के लिए (y=0), इसलिए (x-8=0) से (x=8) मिलता है। ग्राफ (x)-अक्ष को (8) पर काटता है।
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रेखा (y=x+9) का शून्यक क्या होगा?
What will be the zero of the line (y=x+9)?
#linear-polynomial
#negative-zero
#x-intercept
#polynomials
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A (9)
B (-9)
C (0)
D (18)
Explanation opens after your attempt
Step 1
Concept
For the zero, (x+9=0), so (x=-9). Do not make a sign error.
Step 2
Why this answer is correct
The correct answer is B. (-9). For the zero, (x+9=0), so (x=-9). Do not make a sign error.
Step 3
Exam Tip
शून्यक के लिए (x+9=0), इसलिए (x=-9)। चिह्न बदलने की गलती न करें।
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यदि (p(x)=2x+6), तो ग्राफ का (x)-अक्ष से कटाव किस (x)-मान पर होगा?
If (p(x)=2x+6), at which (x)-value will the graph cut the (x)-axis?
#linear-polynomial
#graphical-zero
#value-test
#easy
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A (-3)
B (3)
C (6)
D (-6)
Explanation opens after your attempt
Step 1
Concept
On the (x)-axis, (p(x)=0), so (2x+6=0) gives (x=-3). This is the graphical zero.
Step 2
Why this answer is correct
The correct answer is A. (-3). On the (x)-axis, (p(x)=0), so (2x+6=0) gives (x=-3). This is the graphical zero.
Step 3
Exam Tip
(x)-अक्ष पर (p(x)=0), इसलिए (2x+6=0) से (x=-3)। यही ग्राफीय शून्यक है।
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यदि ग्राफ (x)-अक्ष को ((10,0)) पर काटता है, तो कौन-सा कथन सही है?
If a graph cuts the (x)-axis at ((10,0)), which statement is correct?
#x-intercept
#zero
#coordinate
#graph
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A (10) शून्यक है / (10) is a zero
B (0) शून्यक है / (0) is a zero
C (-10) शून्यक है / (-10) is a zero
D (10) स्थिर पद है / (10) is the constant term
Explanation opens after your attempt
Correct Answer
A. (10) शून्यक है / (10) is a zero
Step 1
Concept
The (x)-coordinate of the intersection point is (10). Therefore (10) is a zero of the polynomial.
Step 2
Why this answer is correct
The correct answer is A. (10) शून्यक है / (10) is a zero. The (x)-coordinate of the intersection point is (10). Therefore (10) is a zero of the polynomial.
Step 3
Exam Tip
कटाव बिंदु का (x)-निर्देशांक (10) है। इसलिए (10) बहुपद का शून्यक है।
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यदि ग्राफ ((0,7)) से गुजरता है, तो क्या इससे (0) शून्यक सिद्ध होता है?
If a graph passes through ((0,7)), does it prove that (0) is a zero?
#common-mistake
#y-intercept
#zeroes
#graph
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A नहीं, क्योंकि (y=7) है / No, because (y=7)
B हाँ, क्योंकि (x=0) है / Yes, because (x=0)
C हाँ, क्योंकि यह (y)-अक्ष पर है / Yes, because it is on the (y)-axis
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Correct Answer
A. नहीं, क्योंकि (y=7) है / No, because (y=7)
Step 1
Concept
For a zero, (y=0) is needed. In ((0,7)), (y=7), so (0) is not a zero.
Step 2
Why this answer is correct
The correct answer is A. नहीं, क्योंकि (y=7) है / No, because (y=7). For a zero, (y=0) is needed. In ((0,7)), (y=7), so (0) is not a zero.
Step 3
Exam Tip
शून्यक के लिए (y=0) चाहिए। ((0,7)) में (y=7) है, इसलिए (0) शून्यक नहीं है।
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यदि बहुपद का ग्राफ (x)-अक्ष को ((-7,0)), ((0,0)), और ((4,0)) पर काटता है, तो शून्यक कौन-से हैं?
If the graph of a polynomial cuts the (x)-axis at ((-7,0)), ((0,0)), and ((4,0)), what are the zeroes?
#multiple-zeroes
#x-axis
#coordinates
#easy
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A (-7), (0), (4)
B (7), (0), (-4)
C (-7), (4), (7)
D (0), (0), (4)
Explanation opens after your attempt
Correct Answer
A. (-7), (0), (4)
Step 1
Concept
The zeroes are the (x)-coordinates of these points. Hence the zeroes are (-7), (0), and (4).
Step 2
Why this answer is correct
The correct answer is A. (-7), (0), (4). The zeroes are the (x)-coordinates of these points. Hence the zeroes are (-7), (0), and (4).
Step 3
Exam Tip
शून्यक इन बिंदुओं के (x)-निर्देशांक हैं। इसलिए शून्यक (-7), (0), और (4) होंगे।
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किसी स्थिर अशून्य बहुपद (p(x)=-3) का ग्राफ (x)-अक्ष को क्यों नहीं काटता?
Why does the graph of the non-zero constant polynomial (p(x)=-3) not cut the (x)-axis?
#constant-polynomial
#no-zero
#x-axis
#easy
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A क्योंकि (y) हमेशा (-3) रहता है / Because (y) always remains (-3)
B क्योंकि (x) हमेशा (-3) रहता है / Because (x) always remains (-3)
C क्योंकि ग्राफ पर कोई बिंदु नहीं होता / Because the graph has no point
D क्योंकि यह परवलय है / Because it is a parabola
Explanation opens after your attempt
Correct Answer
A. क्योंकि (y) हमेशा (-3) रहता है / Because (y) always remains (-3)
Step 1
Concept
For (p(x)=-3), the (y)-value is never (0). So the graph does not cut the (x)-axis and has no zero.
Step 2
Why this answer is correct
The correct answer is A. क्योंकि (y) हमेशा (-3) रहता है / Because (y) always remains (-3). For (p(x)=-3), the (y)-value is never (0). So the graph does not cut the (x)-axis and has no zero.
Step 3
Exam Tip
(p(x)=-3) का (y)-मान कभी (0) नहीं होता। इसलिए ग्राफ (x)-अक्ष को नहीं काटता और कोई शून्यक नहीं है।
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यदि (p(c)=0), तो (c) को क्या कहते हैं?
If (p(c)=0), what is (c) called?
#definition
#zero-of-polynomial
#p-of-c
#easy
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A बहुपद का शून्यक / Zero of the polynomial
B बहुपद का घातांक / Degree of the polynomial
C बहुपद का स्थिर पद / Constant term of the polynomial
D बहुपद का गुणांक / Coefficient of the polynomial
Explanation opens after your attempt
Correct Answer
A. बहुपद का शून्यक / Zero of the polynomial
Step 1
Concept
The value for which the polynomial becomes (0) is called a zero. Therefore (c) is a zero of the polynomial.
Step 2
Why this answer is correct
The correct answer is A. बहुपद का शून्यक / Zero of the polynomial. The value for which the polynomial becomes (0) is called a zero. Therefore (c) is a zero of the polynomial.
Step 3
Exam Tip
जिस मान पर बहुपद का मान (0) हो, वह शून्यक कहलाता है। इसलिए (c) बहुपद का शून्यक है।
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ग्राफ में बिंदु ((-8,0)) दिखने पर बहुपद का कौन-सा मान शून्य होगा?
If the point ((-8,0)) appears on the graph, which value of the polynomial input gives zero?
#negative-zero
#coordinate-reading
#x-intercept
#polynomials
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A (x=-8)
B (x=8)
C (x=0)
D (x=-1)
Explanation opens after your attempt
Step 1
Concept
The point ((-8,0)) means (y=0) at (x=-8). So (x=-8) makes the polynomial zero.
Step 2
Why this answer is correct
The correct answer is A. (x=-8). The point ((-8,0)) means (y=0) at (x=-8). So (x=-8) makes the polynomial zero.
Step 3
Exam Tip
((-8,0)) का अर्थ है (x=-8) पर (y=0)। इसलिए (x=-8) बहुपद को शून्य बनाता है।
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यदि ग्राफ (x)-अक्ष को (x=2) और (x=9) पर काटता है, तो (p(2)) और (p(9)) के मान क्या होंगे?
If a graph cuts the (x)-axis at (x=2) and (x=9), what will be the values of (p(2)) and (p(9))?
#function-values
#x-intercepts
#zeroes
#easy
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A दोनों (0) / Both (0)
B दोनों (1) / Both (1)
C (p(2)=2) और (p(9)=9) / (p(2)=2) and (p(9)=9)
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Correct Answer
A. दोनों (0) / Both (0)
Step 1
Concept
On the (x)-axis, (y=0). Therefore the polynomial value at both these (x)-values is (0).
Step 2
Why this answer is correct
The correct answer is A. दोनों (0) / Both (0). On the (x)-axis, (y=0). Therefore the polynomial value at both these (x)-values is (0).
Step 3
Exam Tip
(x)-अक्ष पर (y=0) होता है। इसलिए इन दोनों (x)-मानों पर बहुपद का मान (0) होगा।
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यदि किसी परवलय का शीर्ष ((-2,0)) पर है और वह (x)-अक्ष को वहीं छूता है, तो शून्यक क्या होगा?
If the vertex of a parabola is at ((-2,0)) and it touches the (x)-axis there, what is the zero?
#vertex
#parabola
#touching-x-axis
#zero
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A (-2)
B (2)
C (0)
D दो शून्यक होंगे / There will be two zeroes
Explanation opens after your attempt
Step 1
Concept
The parabola meets the (x)-axis only at ((-2,0)). Hence its real zero is (-2).
Step 2
Why this answer is correct
The correct answer is A. (-2). The parabola meets the (x)-axis only at ((-2,0)). Hence its real zero is (-2).
Step 3
Exam Tip
परवलय (x)-अक्ष से केवल ((-2,0)) पर मिलता है। इसलिए उसका वास्तविक शून्यक (-2) है।
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किस ग्राफ से शून्यक (1) और (-6) मिलेंगे?
Which graph will give zeroes (1) and (-6)?
#graph-from-zeroes
#x-intercepts
#polynomial-graph
#easy
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A जो (x)-अक्ष को ((1,0)) और ((-6,0)) पर काटे / One that cuts the (x)-axis at ((1,0)) and ((-6,0))
B जो (y)-अक्ष को ((1,0)) और ((-6,0)) पर काटे / One that cuts the (y)-axis at ((1,0)) and ((-6,0))
C जो (x)-अक्ष को ((0,1)) और ((0,-6)) पर काटे / One that cuts the (x)-axis at ((0,1)) and ((0,-6))
D जो (x)-अक्ष को न काटे / One that does not cut the (x)-axis
Explanation opens after your attempt
Correct Answer
A. जो (x)-अक्ष को ((1,0)) और ((-6,0)) पर काटे / One that cuts the (x)-axis at ((1,0)) and ((-6,0))
Step 1
Concept
If the zeroes are (1) and (-6), the graph cuts the (x)-axis at those (x)-values. So the points are ((1,0)) and ((-6,0)).
Step 2
Why this answer is correct
The correct answer is A. जो (x)-अक्ष को ((1,0)) और ((-6,0)) पर काटे / One that cuts the (x)-axis at ((1,0)) and ((-6,0)). If the zeroes are (1) and (-6), the graph cuts the (x)-axis at those (x)-values. So the points are ((1,0)) and ((-6,0)).
Step 3
Exam Tip
शून्यक (1) और (-6) होने पर ग्राफ (x)-अक्ष को इन्हीं (x)-मानों पर काटेगा। इसलिए बिंदु ((1,0)) और ((-6,0)) होंगे।
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यदि कोई ग्राफ (x)-अक्ष को केवल छूता है, तो क्या वह बिंदु शून्यक देगा?
If a graph only touches the (x)-axis, will that point give a zero?
#touching-x-axis
#zeroes
#concept
#easy
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A हाँ / Yes
B नहीं / No
C केवल रेखा में / Only for a line
D केवल तब जब (y=1) हो / Only when (y=1)
Explanation opens after your attempt
Correct Answer
A. हाँ / Yes
Step 1
Concept
Even when the graph touches, the point lies on the (x)-axis and (y=0). Therefore that point gives a zero.
Step 2
Why this answer is correct
The correct answer is A. हाँ / Yes. Even when the graph touches, the point lies on the (x)-axis and (y=0). Therefore that point gives a zero.
Step 3
Exam Tip
छूने पर भी बिंदु (x)-अक्ष पर होता है और (y=0) होता है। इसलिए वह बिंदु शून्यक देता है।
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यदि ग्राफ (x)-अक्ष के नीचे पूरा बना है और (x)-अक्ष को नहीं छूता, तो वास्तविक शून्यक कितने हैं?
If a graph lies completely below the (x)-axis and does not touch it, how many real zeroes does it have?
#no-real-zero
#below-x-axis
#graph
#easy
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A (0)
B (1)
C (2)
D अनंत / Infinite
Explanation opens after your attempt
Step 1
Concept
For a real zero, the graph must meet the (x)-axis. If it stays below and does not touch it, there is no real zero.
Step 2
Why this answer is correct
The correct answer is A. (0). For a real zero, the graph must meet the (x)-axis. If it stays below and does not touch it, there is no real zero.
Step 3
Exam Tip
वास्तविक शून्यक के लिए ग्राफ का (x)-अक्ष से मिलना जरूरी है। नीचे रहने और न छूने पर कोई वास्तविक शून्यक नहीं होगा।
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यदि (p(5)\neq 0), तो (5) के बारे में क्या कहा जाएगा?
If (p(5)\neq 0), what can be said about (5)?
#not-zero
#value-test
#polynomial
#easy
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A (5) शून्यक नहीं है / (5) is not a zero
B (5) शून्यक है / (5) is a zero
C (5) हमेशा दोहरा शून्यक है / (5) is always a repeated zero
D जानकारी अपूर्ण है / Information is incomplete
Explanation opens after your attempt
Correct Answer
A. (5) शून्यक नहीं है / (5) is not a zero
Step 1
Concept
For (5) to be a zero, (p(5)=0) is necessary. If (p(5)\neq 0), then (5) is not a zero.
Step 2
Why this answer is correct
The correct answer is A. (5) शून्यक नहीं है / (5) is not a zero. For (5) to be a zero, (p(5)=0) is necessary. If (p(5)\neq 0), then (5) is not a zero.
Step 3
Exam Tip
शून्यक होने के लिए (p(5)=0) जरूरी है। यदि (p(5)\neq 0), तो (5) शून्यक नहीं है।
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यदि (p(-10)=0), तो (x)-अक्ष पर संबंधित बिंदु कौन-सा होगा?
If (p(-10)=0), which corresponding point will be on the (x)-axis?
#x-axis-point
#function-value
#negative-zero
#easy
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A ((-10,0))
B ((10,0))
C ((0,-10))
D ((-10,-10))
Explanation opens after your attempt
Correct Answer
A. ((-10,0))
Step 1
Concept
(p(-10)=0) means (y=0) at (x=-10). Therefore the point on the (x)-axis is ((-10,0)).
Step 2
Why this answer is correct
The correct answer is A. ((-10,0)). (p(-10)=0) means (y=0) at (x=-10). Therefore the point on the (x)-axis is ((-10,0)).
Step 3
Exam Tip
(p(-10)=0) का अर्थ है (x=-10) पर (y=0)। इसलिए (x)-अक्ष पर बिंदु ((-10,0)) होगा।
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किसी बहुपद के ग्राफ में (x)-अक्ष से अलग-अलग मिलने वाले बिंदुओं की संख्या क्या बताती है?
What does the number of distinct meeting points with the (x)-axis tell in a polynomial graph?
#number-of-zeroes
#x-axis
#graphical-meaning
#concept
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A वास्तविक शून्यकों की संख्या / Number of real zeroes
B केवल स्थिर पद / Only constant term
C केवल (y)-अवरोध / Only (y)-intercept
D गुणांकों का योग / Sum of coefficients
Explanation opens after your attempt
Correct Answer
A. वास्तविक शून्यकों की संख्या / Number of real zeroes
Step 1
Concept
The number of distinct points where the graph meets the (x)-axis gives the number of real zeroes. This is the main graphical rule.
Step 2
Why this answer is correct
The correct answer is A. वास्तविक शून्यकों की संख्या / Number of real zeroes. The number of distinct points where the graph meets the (x)-axis gives the number of real zeroes. This is the main graphical rule.
Step 3
Exam Tip
ग्राफ जितनी बार अलग-अलग (x)-अक्ष से मिलता है, उतने वास्तविक शून्यक होते हैं। यह ग्राफीय अर्थ का मुख्य नियम है।
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यदि (p(x)=4) है, तो ग्राफ (x)-अक्ष से कैसा संबंध रखेगा?
If (p(x)=4), how is the graph related to the (x)-axis?
#constant-polynomial
#parallel-line
#no-zero
#easy
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A यह (x)-अक्ष के समानांतर होगा और उसे नहीं काटेगा / It is parallel to the (x)-axis and does not cut it
B यह (x)-अक्ष को चार बार काटेगा / It cuts the (x)-axis four times
C यह मूल बिंदु से गुजरेगा / It passes through the origin
D यह परवलय होगा / It is a parabola
Explanation opens after your attempt
Correct Answer
A. यह (x)-अक्ष के समानांतर होगा और उसे नहीं काटेगा / It is parallel to the (x)-axis and does not cut it
Step 1
Concept
In (p(x)=4), (y) is always (4) and never (0). Hence it has no zero.
Step 2
Why this answer is correct
The correct answer is A. यह (x)-अक्ष के समानांतर होगा और उसे नहीं काटेगा / It is parallel to the (x)-axis and does not cut it. In (p(x)=4), (y) is always (4) and never (0). Hence it has no zero.
Step 3
Exam Tip
(p(x)=4) में (y) हमेशा (4) है और कभी (0) नहीं होता। इसलिए इसका कोई शून्यक नहीं है।
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यदि (p(x)=x), तो ग्राफ का शून्यक क्या है?
If (p(x)=x), what is the zero of the graph?
#linear-polynomial
#origin
#zero
#easy
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A (0)
B (1)
C (-1)
D कोई नहीं / None
Explanation opens after your attempt
Step 1
Concept
For the zero, (x=0) because (p(x)=x). The graph passes through the origin.
Step 2
Why this answer is correct
The correct answer is A. (0). For the zero, (x=0) because (p(x)=x). The graph passes through the origin.
Step 3
Exam Tip
शून्यक के लिए (x=0) होना चाहिए क्योंकि (p(x)=x)। ग्राफ मूल बिंदु से गुजरता है।
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यदि किसी ग्राफ के शून्यक (-1), (3), और (8) हैं, तो ग्राफ (x)-अक्ष को किन बिंदुओं पर काटेगा?
If the zeroes of a graph are (-1), (3), and (8), at which points will it cut the (x)-axis?
#zeroes-to-points
#x-intercepts
#graph
#easy
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A ((-1,0)), ((3,0)), ((8,0))
B ((0,-1)), ((0,3)), ((0,8))
C ((1,0)), ((-3,0)), ((-8,0))
D ((-1,1)), ((3,3)), ((8,8))
Explanation opens after your attempt
Correct Answer
A. ((-1,0)), ((3,0)), ((8,0))
Step 1
Concept
Use the zeroes as (x)-coordinates and take (y=0). So the intersection points are ((-1,0)), ((3,0)), and ((8,0)).
Step 2
Why this answer is correct
The correct answer is A. ((-1,0)), ((3,0)), ((8,0)). Use the zeroes as (x)-coordinates and take (y=0). So the intersection points are ((-1,0)), ((3,0)), and ((8,0)).
Step 3
Exam Tip
शून्यकों को (x)-निर्देशांक बनाकर (y=0) लिया जाता है। इसलिए कटाव बिंदु ((-1,0)), ((3,0)), और ((8,0)) होंगे।
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यदि किसी परवलय के दो वास्तविक शून्यक हैं, तो वह (x)-अक्ष से कैसे मिलेगा?
If a parabola has two real zeroes, how will it meet the (x)-axis?
#quadratic
#two-real-zeroes
#parabola
#graph
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A दो अलग-अलग बिंदुओं पर काटेगा / It will cut at two distinct points
B कहीं नहीं मिलेगा / It will not meet anywhere
C एक ही बिंदु पर छुएगा / It will touch at one point
D पूरे (x)-अक्ष पर होगा / It will lie on the whole (x)-axis
Explanation opens after your attempt
Correct Answer
A. दो अलग-अलग बिंदुओं पर काटेगा / It will cut at two distinct points
Step 1
Concept
Two real zeroes show two distinct (x)-axis intersections. Hence the parabola cuts the (x)-axis at two points.
Step 2
Why this answer is correct
The correct answer is A. दो अलग-अलग बिंदुओं पर काटेगा / It will cut at two distinct points. Two real zeroes show two distinct (x)-axis intersections. Hence the parabola cuts the (x)-axis at two points.
Step 3
Exam Tip
दो वास्तविक शून्यक दो अलग (x)-अक्ष कटाव बताते हैं। इसलिए परवलय (x)-अक्ष को दो बिंदुओं पर काटेगा।
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यदि किसी परवलय का एक ही वास्तविक शून्यक है, तो ग्राफ (x)-अक्ष से कैसे मिलेगा?
If a parabola has exactly one real zero, how will its graph meet the (x)-axis?
#one-real-zero
#parabola
#tangent-case
#easy
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A एक बिंदु पर छुएगा / It will touch at one point
B दो बिंदुओं पर काटेगा / It will cut at two points
C कहीं नहीं मिलेगा / It will not meet
D चार बिंदुओं पर काटेगा / It will cut at four points
Explanation opens after your attempt
Correct Answer
A. एक बिंदु पर छुएगा / It will touch at one point
Step 1
Concept
One real zero means the graph meets the (x)-axis at only one point. For a parabola, this is usually the touching case.
Step 2
Why this answer is correct
The correct answer is A. एक बिंदु पर छुएगा / It will touch at one point. One real zero means the graph meets the (x)-axis at only one point. For a parabola, this is usually the touching case.
Step 3
Exam Tip
एक वास्तविक शून्यक का अर्थ है ग्राफ (x)-अक्ष से केवल एक बिंदु पर मिलता है। परवलय में यह सामान्यतः छूने की स्थिति होती है।
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यदि ग्राफ (x)-अक्ष को ((2,0)) पर काटता और ((5,0)) पर छूता है, तो अलग वास्तविक शून्यक कितने हैं?
If a graph cuts the (x)-axis at ((2,0)) and touches it at ((5,0)), how many distinct real zeroes are there?
#distinct-real-zeroes
#touching-cutting
#x-axis
#easy
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A दो / Two
B एक / One
C तीन / Three
D कोई नहीं / None
Explanation opens after your attempt
Step 1
Concept
Both cutting and touching mean meeting the (x)-axis. There are two distinct points, so there are two distinct real zeroes.
Step 2
Why this answer is correct
The correct answer is A. दो / Two. Both cutting and touching mean meeting the (x)-axis. There are two distinct points, so there are two distinct real zeroes.
Step 3
Exam Tip
कटना और छूना दोनों (x)-अक्ष से मिलना है। दो अलग बिंदु हैं, इसलिए दो अलग वास्तविक शून्यक हैं।
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यदि ग्राफ (x)-अक्ष को ((r,0)) पर छूता है, तो (r) के बारे में क्या कहा जाएगा?
If a graph touches the (x)-axis at ((r,0)), what can be said about (r)?
#general-touching-point
#zeroes
#x-axis
#easy
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A (r) शून्यक है / (r) is a zero
B (r) स्थिर पद है / (r) is the constant term
C (r) घात है / (r) is the degree
D (r) शून्यक नहीं है / (r) is not a zero
Explanation opens after your attempt
Correct Answer
A. (r) शून्यक है / (r) is a zero
Step 1
Concept
Even when the graph touches, (y=0). Therefore the (x)-coordinate (r) of ((r,0)) is a zero.
Step 2
Why this answer is correct
The correct answer is A. (r) शून्यक है / (r) is a zero. Even when the graph touches, (y=0). Therefore the (x)-coordinate (r) of ((r,0)) is a zero.
Step 3
Exam Tip
छूने पर भी (y=0) होता है। इसलिए ((r,0)) का (x)-निर्देशांक (r) शून्यक है।
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यदि (p(12)=0), तो (12) को ग्राफ पर कैसे देखा जाएगा?
If (p(12)=0), how will (12) be seen on the graph?
#function-value
#graphical-meaning
#zeroes
#easy
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A ग्राफ (x)-अक्ष को (x=12) पर काटेगा या छुएगा / The graph will cut or touch the (x)-axis at (x=12)
B ग्राफ (y)-अक्ष को (y=12) पर काटेगा / The graph will cut the (y)-axis at (y=12)
C ग्राफ (x=0) पर ही होगा / The graph will only be at (x=0)
D ग्राफ नहीं बनेगा / No graph will be formed
Explanation opens after your attempt
Correct Answer
A. ग्राफ (x)-अक्ष को (x=12) पर काटेगा या छुएगा / The graph will cut or touch the (x)-axis at (x=12)
Step 1
Concept
(p(12)=0) means (y=0) at (x=12). So the graph will meet the (x)-axis there.
Step 2
Why this answer is correct
The correct answer is A. ग्राफ (x)-अक्ष को (x=12) पर काटेगा या छुएगा / The graph will cut or touch the (x)-axis at (x=12). (p(12)=0) means (y=0) at (x=12). So the graph will meet the (x)-axis there.
Step 3
Exam Tip
(p(12)=0) का अर्थ है (x=12) पर (y=0)। इसलिए ग्राफ (x)-अक्ष से वहाँ मिलेगा।
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किस बिंदु पर ग्राफ होने से (x=11) शून्यक सिद्ध होगा?
Which point on the graph proves that (x=11) is a zero?
#point-identification
#zeroes
#x-axis
#graph
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A ((11,0))
B ((0,11))
C ((11,1))
D ((-11,0))
Explanation opens after your attempt
Correct Answer
A. ((11,0))
Step 1
Concept
For (x=11) to be a zero, (y=0) is needed. So the point must be ((11,0)).
Step 2
Why this answer is correct
The correct answer is A. ((11,0)). For (x=11) to be a zero, (y=0) is needed. So the point must be ((11,0)).
Step 3
Exam Tip
(x=11) शून्यक होने के लिए (y=0) चाहिए। इसलिए बिंदु ((11,0)) होना चाहिए।
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किस बिंदु पर ग्राफ होने से (x=-2) शून्यक सिद्ध होगा?
Which point on the graph proves that (x=-2) is a zero?
#negative-zero
#point-reading
#x-intercept
#easy
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A ((-2,0))
B ((2,0))
C ((0,-2))
D ((-2,2))
Explanation opens after your attempt
Correct Answer
A. ((-2,0))
Step 1
Concept
For (x=-2) to be a zero, (y=0) at that point. Hence the correct point is ((-2,0)).
Step 2
Why this answer is correct
The correct answer is A. ((-2,0)). For (x=-2) to be a zero, (y=0) at that point. Hence the correct point is ((-2,0)).
Step 3
Exam Tip
(x=-2) शून्यक होने के लिए उस बिंदु पर (y=0) होना चाहिए। इसलिए सही बिंदु ((-2,0)) है।
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यदि (p(x)) का ग्राफ मूल बिंदु से गुजरता है, तो कौन-सा मान शून्यक है?
If the graph of (p(x)) passes through the origin, which value is a zero?
#origin
#zeroes
#graph
#polynomials
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A (0)
B (1
C (-1)
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Step 1
Concept
The origin is ((0,0)), so (p(x)=0) at (x=0). Hence (0) is a zero.
Step 2
Why this answer is correct
The correct answer is A. (0). The origin is ((0,0)), so (p(x)=0) at (x=0). Hence (0) is a zero.
Step 3
Exam Tip
मूल बिंदु ((0,0)) है, इसलिए (x=0) पर (p(x)=0)। अतः (0) शून्यक है।
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यदि बहुपद के ग्राफ में (x)-अक्ष से मिलने वाले बिंदु ((-9,0)), ((-1,0)), और ((3,0)) हैं, तो वास्तविक शून्यक कितने हैं?
If the points where a polynomial graph meets the (x)-axis are ((-9,0)), ((-1,0)), and ((3,0)), how many real zeroes are there?
#counting-zeroes
#x-intercepts
#graph-reading
#easy
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A तीन / Three
B दो / Two
C एक / One
D कोई नहीं / None
Explanation opens after your attempt
Correct Answer
A. तीन / Three
Step 1
Concept
Three distinct (x)-axis points show three distinct real zeroes. Their (x)-coordinates are the zeroes.
Step 2
Why this answer is correct
The correct answer is A. तीन / Three. Three distinct (x)-axis points show three distinct real zeroes. Their (x)-coordinates are the zeroes.
Step 3
Exam Tip
तीन अलग (x)-अक्ष बिंदु तीन अलग वास्तविक शून्यक बताते हैं। उनके (x)-निर्देशांक ही शून्यक हैं।
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यदि किसी ग्राफ में ((4,2)) बिंदु है, तो क्या (4) शून्यक है?
If a graph has the point ((4,2)), is (4) a zero?
#point-test
#not-zero
#graph
#easy
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A नहीं / No
B हाँ / Yes
C केवल यदि बहुपद द्विघात हो / Only if the polynomial is quadratic
D केवल यदि ग्राफ रेखा हो / Only if the graph is a line
Explanation opens after your attempt
Correct Answer
A. नहीं / No
Step 1
Concept
In ((4,2)), (y=2), not (0). Therefore (x=4) is not a zero.
Step 2
Why this answer is correct
The correct answer is A. नहीं / No. In ((4,2)), (y=2), not (0). Therefore (x=4) is not a zero.
Step 3
Exam Tip
((4,2)) में (y=2) है, (0) नहीं। इसलिए (x=4) शून्यक नहीं है।
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यदि ग्राफ (x)-अक्ष को ((m,0)) और ((n,0)) पर काटता है, जहाँ \(m\neq n\), तो वास्तविक शून्यकों की संख्या क्या होगी?
If a graph cuts the (x)-axis at ((m,0)) and ((n,0)), where \(m\neq n\), how many real zeroes will it have?
#general-zeroes
#distinct-points
#x-axis
#easy
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A दो / Two
B एक / One
C कोई नहीं / None
D अनंत / Infinite
Explanation opens after your attempt
Step 1
Concept
Two distinct intersection points give two distinct real zeroes. Here the zeroes will be (m) and (n).
Step 2
Why this answer is correct
The correct answer is A. दो / Two. Two distinct intersection points give two distinct real zeroes. Here the zeroes will be (m) and (n).
Step 3
Exam Tip
दो अलग कटाव बिंदु दो अलग वास्तविक शून्यक देते हैं। यहाँ शून्यक (m) और (n) होंगे।
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ग्राफ में शून्यक देखने के लिए किस अक्ष पर ध्यान देना चाहिए?
Which axis should be observed to see the zeroes on a graph?
#x-axis
#zeroes
#graphical-meaning
#easy
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A (x)-अक्ष / (x)-axis
B (y)-अक्ष / (y)-axis
C दोनों अक्ष हमेशा / Both axes always
D कोई अक्ष नहीं / No axis
Explanation opens after your attempt
Correct Answer
A. (x)-अक्ष / (x)-axis
Step 1
Concept
Zeroes are obtained from the points where the graph meets the (x)-axis. So focus on the (x)-axis while reading the graph.
Step 2
Why this answer is correct
The correct answer is A. (x)-अक्ष / (x)-axis. Zeroes are obtained from the points where the graph meets the (x)-axis. So focus on the (x)-axis while reading the graph.
Step 3
Exam Tip
शून्यक (x)-अक्ष से मिलने वाले बिंदुओं से मिलते हैं। इसलिए ग्राफ पढ़ते समय (x)-अक्ष पर ध्यान दें।
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यदि ग्राफ (x)-अक्ष को ((7,0)) पर काटता है, तो (p(7)) का मान क्या होगा?
If the graph cuts the (x)-axis at ((7,0)), what will be the value of (p(7))?
#p-value
#x-axis
#zeroes
#easy
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A (0)
B (7)
C (-7)
D (1)
Explanation opens after your attempt
Step 1
Concept
On the (x)-axis, (y=0). Therefore at ((7,0)), (p(7)=0).
Step 2
Why this answer is correct
The correct answer is A. (0). On the (x)-axis, (y=0). Therefore at ((7,0)), (p(7)=0).
Step 3
Exam Tip
(x)-अक्ष पर (y=0) होता है। इसलिए ((7,0)) पर (p(7)=0) होगा।
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यदि (p(-4)=0), तो ग्राफ (x)-अक्ष से कहाँ मिलेगा?
If (p(-4)=0), where will the graph meet the (x)-axis?
#negative-zero
#function-value
#x-axis
#easy
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A ((-4,0))
B ((4,0))
C ((0,-4))
D ((-4,4))
Explanation opens after your attempt
Correct Answer
A. ((-4,0))
Step 1
Concept
(p(-4)=0) means (y=0) when (x=-4). Therefore the graph meets the (x)-axis at ((-4,0)).
Step 2
Why this answer is correct
The correct answer is A. ((-4,0)). (p(-4)=0) means (y=0) when (x=-4). Therefore the graph meets the (x)-axis at ((-4,0)).
Step 3
Exam Tip
(p(-4)=0) बताता है कि (x=-4) पर (y=0) है। इसलिए ग्राफ (x)-अक्ष से ((-4,0)) पर मिलेगा।
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यदि किसी बहुपद का ग्राफ (x)-अक्ष को बिल्कुल दो बार छूता या काटता है, तो वास्तविक शून्यकों की संख्या क्या होगी?
If a polynomial graph touches or cuts the (x)-axis exactly two times, how many real zeroes will it have?
#touch-or-cut
#counting-zeroes
#x-axis
#easy
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A दो / Two
B एक / One
C तीन / Three
D कोई नहीं / None
Explanation opens after your attempt
Step 1
Concept
Each distinct meeting with the (x)-axis gives one real zero. If it meets twice, it has two real zeroes.
Step 2
Why this answer is correct
The correct answer is A. दो / Two. Each distinct meeting with the (x)-axis gives one real zero. If it meets twice, it has two real zeroes.
Step 3
Exam Tip
(x)-अक्ष से हर अलग मिलन एक वास्तविक शून्यक देता है। दो बार मिलने पर दो वास्तविक शून्यक होंगे।
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यदि किसी बहुपद का कोई वास्तविक शून्यक नहीं है, तो उसका ग्राफ (x)-अक्ष के साथ क्या करेगा?
If a polynomial has no real zero, what will its graph do with the (x)-axis?
#no-real-zero
#graph
#x-axis
#concept
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A न तो काटेगा न छुएगा / It will neither cut nor touch it
B हमेशा दो बार काटेगा / It will always cut twice
C हमेशा एक बार छुएगा / It will always touch once
D पूरे (x)-अक्ष पर रहेगा / It will lie on the whole (x)-axis
Explanation opens after your attempt
Correct Answer
A. न तो काटेगा न छुएगा / It will neither cut nor touch it
Step 1
Concept
A real zero appears when the graph meets the (x)-axis. With no real zero, the graph will not meet the (x)-axis.
Step 2
Why this answer is correct
The correct answer is A. न तो काटेगा न छुएगा / It will neither cut nor touch it. A real zero appears when the graph meets the (x)-axis. With no real zero, the graph will not meet the (x)-axis.
Step 3
Exam Tip
वास्तविक शून्यक (x)-अक्ष से मिलने पर दिखता है। कोई वास्तविक शून्यक न होने पर ग्राफ (x)-अक्ष से नहीं मिलेगा।
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यदि (p(x)) का ग्राफ (x)-अक्ष को ((u,0)), ((v,0)), और ((w,0)) पर काटता है, तो शून्यक कौन-से हैं?
If the graph of (p(x)) cuts the (x)-axis at ((u,0)), ((v,0)), and ((w,0)), what are the zeroes?
#general-zeroes
#coordinates
#x-intercepts
#polynomials
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A (u), (v), (w)
B (0), (0), (0)
C (-u), (-v), (-w)
D (u+v+w)
Explanation opens after your attempt
Correct Answer
A. (u), (v), (w)
Step 1
Concept
Zeroes are the (x)-coordinates of the (x)-axis intersections. Therefore the zeroes are (u), (v), and (w).
Step 2
Why this answer is correct
The correct answer is A. (u), (v), (w). Zeroes are the (x)-coordinates of the (x)-axis intersections. Therefore the zeroes are (u), (v), and (w).
Step 3
Exam Tip
शून्यक (x)-अक्ष कटावों के (x)-निर्देशांक होते हैं। इसलिए शून्यक (u), (v), और (w) हैं।
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किसी बहुपद (p(x)) का शून्यक आलेख में किससे दर्शाया जाता है?
What represents a zero of a polynomial (p(x)) on its graph?
#polynomials zeroes graph
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A जहाँ आलेख (x)-अक्ष को काटता है / Where the graph cuts the (x)-axis
B जहाँ आलेख (y)-अक्ष को काटता है / Where the graph cuts the (y)-axis
C आलेख का सबसे ऊँचा बिंदु / The highest point of the graph
D आलेख का कोई भी बिंदु / Any point on the graph
Explanation opens after your attempt
Correct Answer
A. जहाँ आलेख (x)-अक्ष को काटता है / Where the graph cuts the (x)-axis
Step 1
Concept
At a zero (p(x)=0) so the point lies on the (x)-axis. Tip: on the (x)-axis (y=0).
Step 2
Why this answer is correct
The correct answer is A. जहाँ आलेख (x)-अक्ष को काटता है / Where the graph cuts the (x)-axis. At a zero (p(x)=0) so the point lies on the (x)-axis. Tip: on the (x)-axis (y=0).
Step 3
Exam Tip
शून्यक पर (p(x)=0) होता है इसलिए बिंदु (x)-अक्ष पर होता है। टिप: (x)-अक्ष पर (y=0) होता है।
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यदि किसी रैखिक बहुपद का आलेख (x)-अक्ष को एक बार काटता है तो उसके कितने शून्यक होंगे?
If the graph of a linear polynomial cuts the (x)-axis once then how many zeroes does it have?
#polynomials linear graph
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A एक / One
B दो / Two
C शून्य / Zero
D तीन / Three
Explanation opens after your attempt
Step 1
Concept
The number of real zeroes equals the number of times the graph cuts the (x)-axis. Tip: a linear polynomial has at most one zero.
Step 2
Why this answer is correct
The correct answer is A. एक / One. The number of real zeroes equals the number of times the graph cuts the (x)-axis. Tip: a linear polynomial has at most one zero.
Step 3
Exam Tip
जितनी बार आलेख (x)-अक्ष को काटता है उतने वास्तविक शून्यक होते हैं। टिप: रैखिक बहुपद का अधिकतम एक शून्यक होता है।
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यदि द्विघात बहुपद का आलेख (x)-अक्ष को दो अलग-अलग बिंदुओं पर काटता है तो वास्तविक शून्यकों की संख्या क्या होगी?
If the graph of a quadratic polynomial cuts the (x)-axis at two distinct points then what is the number of real zeroes?
#quadratic zeroes graph
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A दो / Two
B एक / One
C शून्य / Zero
D चार / Four
Explanation opens after your attempt
Step 1
Concept
Two intersection points show two real zeroes. Tip: a parabola can cut the (x)-axis at most twice.
Step 2
Why this answer is correct
The correct answer is A. दो / Two. Two intersection points show two real zeroes. Tip: a parabola can cut the (x)-axis at most twice.
Step 3
Exam Tip
दो कटान बिंदु दो वास्तविक शून्यक बताते हैं। टिप: परवलय (x)-अक्ष को अधिकतम दो बार काट सकता है।
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यदि परवलय (x)-अक्ष को केवल स्पर्श करता है तो बहुपद के कितने वास्तविक शून्यक माने जाते हैं?
If a parabola only touches the (x)-axis then how many real zeroes does the polynomial have?
#quadratic tangent zero
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A एक / One
B दो / Two
C शून्य / Zero
D तीन / Three
Explanation opens after your attempt
Step 1
Concept
When it touches the axis there is only one repeated zero. Tip: touching also means meeting the (x)-axis.
Step 2
Why this answer is correct
The correct answer is A. एक / One. When it touches the axis there is only one repeated zero. Tip: touching also means meeting the (x)-axis.
Step 3
Exam Tip
स्पर्श करने पर केवल एक समान शून्यक मिलता है। टिप: छूना भी (x)-अक्ष से मिलना है।
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यदि द्विघात बहुपद का आलेख (x)-अक्ष को कहीं नहीं छूता तो उसके वास्तविक शून्यकों की संख्या क्या होगी?
If the graph of a quadratic polynomial does not meet the (x)-axis anywhere then how many real zeroes does it have?
#quadratic no real zero
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A शून्य / Zero
B एक / One
C दो / Two
D असीमित / Infinite
Explanation opens after your attempt
Correct Answer
A. शून्य / Zero
Step 1
Concept
There is no (x)-axis intersection so there is no real zero. Tip: count only meetings with the (x)-axis.
Step 2
Why this answer is correct
The correct answer is A. शून्य / Zero. There is no (x)-axis intersection so there is no real zero. Tip: count only meetings with the (x)-axis.
Step 3
Exam Tip
कोई (x)-अक्ष कटान नहीं है इसलिए कोई वास्तविक शून्यक नहीं है। टिप: केवल (x)-अक्ष पर मिलने को गिनें।
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किसी बहुपद के आलेख पर बिंदु ((4,0)) है। इससे कौन सा कथन सही है?
The point ((4,0)) lies on the graph of a polynomial. Which statement is correct?
#point zero graph
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A (4) बहुपद का शून्यक है / (4) is a zero of the polynomial
B (0) बहुपद का शून्यक है / (0) is a zero of the polynomial
C (4) (y)-अक्ष कटान है / (4) is the (y)-intercept
D बहुपद स्थिर है / The polynomial is constant
Explanation opens after your attempt
Correct Answer
A. (4) बहुपद का शून्यक है / (4) is a zero of the polynomial
Step 1
Concept
The point ((4,0)) means (p(x)=0) at (x=4). Tip: from ((a,0)) the zero is (a).
Step 2
Why this answer is correct
The correct answer is A. (4) बहुपद का शून्यक है / (4) is a zero of the polynomial. The point ((4,0)) means (p(x)=0) at (x=4). Tip: from ((a,0)) the zero is (a).
Step 3
Exam Tip
((4,0)) का अर्थ है (x=4) पर (p(x)=0)। टिप: ((a,0)) से शून्यक (a) मिलता है।
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यदि बहुपद का आलेख मूल बिंदु ((0,0)) से गुजरता है तो कौन सा शून्यक अवश्य होगा?
If the graph of a polynomial passes through the origin ((0,0)) then which zero is certain?
#origin zero graph
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A (0)
B (1)
C (-1)
D (2)
Explanation opens after your attempt
Step 1
Concept
At the origin (x=0) and (p(x)=0). Tip: a graph through the origin has (0) as a zero.
Step 2
Why this answer is correct
The correct answer is A. (0). At the origin (x=0) and (p(x)=0). Tip: a graph through the origin has (0) as a zero.
Step 3
Exam Tip
मूल बिंदु पर (x=0) और (p(x)=0) होता है। टिप: origin पर जाने वाला आलेख (0) को शून्यक बनाता है।
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यदि आलेख (x)-अक्ष को (-2) पर काटता है तो बहुपद का शून्यक क्या है?
If the graph cuts the (x)-axis at (-2) then what is the zero of the polynomial?
#negative zero graph
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A (-2)
B (2)
C (0)
D (-1)
Explanation opens after your attempt
Step 1
Concept
The (x)-coordinate of the (x)-axis intersection is the zero. Tip: read the sign carefully.
Step 2
Why this answer is correct
The correct answer is A. (-2). The (x)-coordinate of the (x)-axis intersection is the zero. Tip: read the sign carefully.
Step 3
Exam Tip
(x)-अक्ष कटान का (x)-निर्देशांक ही शून्यक होता है। टिप: चिह्न को ध्यान से पढ़ें।
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एक आलेख (x)-अक्ष को (-3) और (5) पर काटता है। इसके वास्तविक शून्यक कौन से हैं?
A graph cuts the (x)-axis at (-3) and (5). What are its real zeroes?
#two zeroes intercepts
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A (-3) और (5) / (-3) and (5)
B (3) और (-5) / (3) and (-5)
C (-3) और (-5) / (-3) and (-5)
D (0) और (5) / (0) and (5)
Explanation opens after your attempt
Correct Answer
A. (-3) और (5) / (-3) and (5)
Step 1
Concept
The (x)-values of the intersection points are the zeroes. Tip: the (y)-value there is (0).
Step 2
Why this answer is correct
The correct answer is A. (-3) और (5) / (-3) and (5). The (x)-values of the intersection points are the zeroes. Tip: the (y)-value there is (0).
Step 3
Exam Tip
कटान बिंदुओं के (x)-मान शून्यक होते हैं। टिप: (y)-मान यहाँ (0) रहता है।
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यदि किसी रैखिक बहुपद का आलेख (x)-अक्ष के समांतर है और उसे नहीं काटता तो उसके कितने शून्यक हैं?
If the graph of a linear polynomial is parallel to the (x)-axis and does not cut it then how many zeroes does it have?
#linear no zero
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A शून्य / Zero
B एक / One
C दो / Two
D असीमित / Infinite
Explanation opens after your attempt
Correct Answer
A. शून्य / Zero
Step 1
Concept
On such a line (p(x)) is never (0). Tip: meeting the (x)-axis is necessary.
Step 2
Why this answer is correct
The correct answer is A. शून्य / Zero. On such a line (p(x)) is never (0). Tip: meeting the (x)-axis is necessary.
Step 3
Exam Tip
ऐसी रेखा पर (p(x)) कभी (0) नहीं होता। टिप: (x)-अक्ष से मिलना जरूरी है।
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बहुपद (p(x)=x-7) का आलेख (x)-अक्ष को किस बिंदु पर काटेगा?
At which point will the graph of (p(x)=x-7) cut the (x)-axis?
#linear polynomial zero
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A ((7,0))
B ((-7,0))
C ((0,7))
D ((0,-7))
Explanation opens after your attempt
Correct Answer
A. ((7,0))
Step 1
Concept
From (x-7=0) we get (x=7). Tip: write the zero as the point ((x,0)).
Step 2
Why this answer is correct
The correct answer is A. ((7,0)). From (x-7=0) we get (x=7). Tip: write the zero as the point ((x,0)).
Step 3
Exam Tip
(x-7=0) से (x=7) मिलता है। टिप: शून्यक को बिंदु ((x,0)) में लिखें।
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बहुपद (p(x)=x+4) के आलेख का (x)-अक्ष कटान बिंदु कौन सा है?
What is the (x)-axis intersection point of the graph of (p(x)=x+4)?
#linear intercept graph
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A ((-4,0))
B ((4,0))
C ((0,4))
D ((0,-4))
Explanation opens after your attempt
Correct Answer
A. ((-4,0))
Step 1
Concept
From (x+4=0) we get (x=-4). Tip: on the (x)-axis the second coordinate is (0).
Step 2
Why this answer is correct
The correct answer is A. ((-4,0)). From (x+4=0) we get (x=-4). Tip: on the (x)-axis the second coordinate is (0).
Step 3
Exam Tip
(x+4=0) से (x=-4) मिलता है। टिप: (x)-अक्ष पर दूसरा निर्देशांक (0) होता है।
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बहुपद (p(x)=2x-6) का शून्यक आलेख में किस (x)-मान पर दिखेगा?
At which (x)-value will the zero of (p(x)=2x-6) appear on the graph?
#linear zero value
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A (3)
B (-3)
C (6)
D (2)
Explanation opens after your attempt
Step 1
Concept
Solving (2x-6=0) gives (x=3). Tip: first put (p(x)=0).
Step 2
Why this answer is correct
The correct answer is A. (3). Solving (2x-6=0) gives (x=3). Tip: first put (p(x)=0).
Step 3
Exam Tip
(2x-6=0) से (x=3) होता है। टिप: पहले (p(x)=0) रखें।
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यदि आलेख (x)-अक्ष को ((6,0)) पर काटता है तो (p(6)) का मान क्या होगा?
If the graph cuts the (x)-axis at ((6,0)) then what is the value of (p(6))?
#function value zero
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A (0)
B (6)
C (1)
D (-6)
Explanation opens after your attempt
Step 1
Concept
On the (x)-axis (y=p(x)=0). Tip: read the function value directly from the intersection point.
Step 2
Why this answer is correct
The correct answer is A. (0). On the (x)-axis (y=p(x)=0). Tip: read the function value directly from the intersection point.
Step 3
Exam Tip
(x)-अक्ष पर (y=p(x)=0) होता है। टिप: कटान बिंदु से फलन मान सीधे पढ़ें।
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यदि (p(-1)=0) है तो बहुपद के आलेख के बारे में कौन सा कथन सही है?
If (p(-1)=0) then which statement about the graph of the polynomial is correct?
#zero point relation
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A आलेख ((-1,0)) से गुजरता है / The graph passes through ((-1,0))
B आलेख ((0,-1)) से गुजरता है / The graph passes through ((0,-1))
C आलेख (y)-अक्ष को नहीं काटता / The graph does not cut the (y)-axis
D आलेख हमेशा सीधी रेखा है / The graph is always a straight line
Explanation opens after your attempt
Correct Answer
A. आलेख ((-1,0)) से गुजरता है / The graph passes through ((-1,0))
Step 1
Concept
The value (p(-1)=0) gives the point ((-1,0)). Tip: connect (p(a)=0) with ((a,0)).
Step 2
Why this answer is correct
The correct answer is A. आलेख ((-1,0)) से गुजरता है / The graph passes through ((-1,0)). The value (p(-1)=0) gives the point ((-1,0)). Tip: connect (p(a)=0) with ((a,0)).
Step 3
Exam Tip
(p(-1)=0) का बिंदु ((-1,0)) है। टिप: (p(a)=0) को ((a,0)) से जोड़ें।
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किसी बहुपद के आलेख में (y)-अक्ष कटान ((0,5)) है। क्या (0) उसका शून्यक है?
The graph of a polynomial has (y)-axis intercept ((0,5)). Is (0) its zero?
#y intercept misconception
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A नहीं क्योंकि (p(0)=5) / No because (p(0)=5)
B हाँ क्योंकि (x=0) है / Yes because (x=0)
C हाँ क्योंकि यह अक्ष पर है / Yes because it is on an axis
D नहीं क्योंकि हर बहुपद का शून्यक नहीं होता / No because no polynomial has a zero
Explanation opens after your attempt
Correct Answer
A. नहीं क्योंकि (p(0)=5) / No because (p(0)=5)
Step 1
Concept
For (0) to be a zero (p(0)) must be (0). Tip: a (y)-axis intercept is not always a zero.
Step 2
Why this answer is correct
The correct answer is A. नहीं क्योंकि (p(0)=5) / No because (p(0)=5). For (0) to be a zero (p(0)) must be (0). Tip: a (y)-axis intercept is not always a zero.
Step 3
Exam Tip
शून्यक के लिए (p(0)) को (0) होना चाहिए। टिप: (y)-अक्ष कटान हमेशा शून्यक नहीं होता।
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आलेख (x)-अक्ष को केवल ((2,0)) पर स्पर्श करता है। शून्यक कौन सा है?
The graph only touches the (x)-axis at ((2,0)). Which is the zero?
#touching point zero
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A (2)
B (0)
C दो और शून्य / Two and zero
D कोई नहीं / None
Explanation opens after your attempt
Step 1
Concept
The (x)-coordinate of the touching point is (2) so the zero is (2). Tip: count a touching point too.
Step 2
Why this answer is correct
The correct answer is A. (2). The (x)-coordinate of the touching point is (2) so the zero is (2). Tip: count a touching point too.
Step 3
Exam Tip
स्पर्श बिंदु का (x)-निर्देशांक (2) है इसलिए शून्यक (2) है। टिप: स्पर्श बिंदु को भी गिनें।
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एक परवलय ऊपर की ओर खुलता है और उसका शीर्ष ((0,3)) है। यदि वह (x)-अक्ष को नहीं काटता तो वास्तविक शून्यक कितने हैं?
A parabola opens upward and has vertex ((0,3)). If it does not cut the (x)-axis then how many real zeroes are there?
#parabola above axis
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A शून्य / Zero
B एक / One
C दो / Two
D तीन / Three
Explanation opens after your attempt
Correct Answer
A. शून्य / Zero
Step 1
Concept
The graph can stay above the (x)-axis so there is no real zero. Tip: if there is no intersection do not write a zero.
Step 2
Why this answer is correct
The correct answer is A. शून्य / Zero. The graph can stay above the (x)-axis so there is no real zero. Tip: if there is no intersection do not write a zero.
Step 3
Exam Tip
आलेख पूरा (x)-अक्ष से ऊपर रह सकता है इसलिए कोई वास्तविक शून्यक नहीं है। टिप: कटान न हो तो शून्यक न लिखें।
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यदि किसी द्विघात बहुपद के वास्तविक शून्यक (1) और (4) हैं तो उसका आलेख (x)-अक्ष को किन बिंदुओं पर काटेगा?
If a quadratic polynomial has real zeroes (1) and (4) then at which points will its graph cut the (x)-axis?
#zeroes to points
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A ((1,0)) और ((4,0)) / ((1,0)) and ((4,0))
B ((0,1)) और ((0,4)) / ((0,1)) and ((0,4))
C ((1,1)) और ((4,4)) / ((1,1)) and ((4,4))
D ((-1,0)) और ((-4,0)) / ((-1,0)) and ((-4,0))
Explanation opens after your attempt
Correct Answer
A. ((1,0)) और ((4,0)) / ((1,0)) and ((4,0))
Step 1
Concept
A zero (a) gives the intersection point ((a,0)). Tip: do not make the zero the (y)-coordinate.
Step 2
Why this answer is correct
The correct answer is A. ((1,0)) और ((4,0)) / ((1,0)) and ((4,0)). A zero (a) gives the intersection point ((a,0)). Tip: do not make the zero the (y)-coordinate.
Step 3
Exam Tip
शून्यक (a) से कटान बिंदु ((a,0)) बनता है। टिप: शून्यक को (y)-निर्देशांक न बनाएं।
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यदि आलेख (x)-अक्ष को ((-5,0)) और ((2,0)) पर काटता है तो शून्यकों का योग क्या है?
If the graph cuts the (x)-axis at ((-5,0)) and ((2,0)) then what is the sum of zeroes?
#sum of zeroes graph
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A (-3)
B (3)
C (7)
D (-7)
Explanation opens after your attempt
Step 1
Concept
The zeroes are (-5) and (2) so the sum is (-3). Tip: first take the (x)-values from the points.
Step 2
Why this answer is correct
The correct answer is A. (-3). The zeroes are (-5) and (2) so the sum is (-3). Tip: first take the (x)-values from the points.
Step 3
Exam Tip
शून्यक (-5) और (2) हैं इसलिए योग (-3) है। टिप: पहले बिंदुओं से (x)-मान लें।
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यदि आलेख (x)-अक्ष को ((-2,0)) और ((3,0)) पर काटता है तो शून्यकों का गुणनफल क्या है?
If the graph cuts the (x)-axis at ((-2,0)) and ((3,0)) then what is the product of zeroes?
#product of zeroes graph
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A (-6)
B (6)
C (1)
D (-1)
Explanation opens after your attempt
Step 1
Concept
The zeroes are (-2) and (3) so the product is (-6). Tip: do not use the (y)-value in the product.
Step 2
Why this answer is correct
The correct answer is A. (-6). The zeroes are (-2) and (3) so the product is (-6). Tip: do not use the (y)-value in the product.
Step 3
Exam Tip
शून्यक (-2) और (3) हैं इसलिए गुणनफल (-6) है। टिप: निर्देशांक का (y)-मान गुणन में न लें।
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आलेख में बिंदु ((0,0)) और ((3,0)) (x)-अक्ष पर हैं। संभावित शून्यक कौन से हैं?
In a graph the points ((0,0)) and ((3,0)) lie on the (x)-axis. What are the possible zeroes?
#origin and intercepts
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A (0) और (3) / (0) and (3)
B (3) और (1) / (3) and (1)
C (0) और (-3) / (0) and (-3)
D केवल (3) / Only (3)
Explanation opens after your attempt
Correct Answer
A. (0) और (3) / (0) and (3)
Step 1
Concept
The (x)-coordinates of both points give zeroes. Tip: the origin can also give a zero.
Step 2
Why this answer is correct
The correct answer is A. (0) और (3) / (0) and (3). The (x)-coordinates of both points give zeroes. Tip: the origin can also give a zero.
Step 3
Exam Tip
दोनों बिंदुओं के (x)-निर्देशांक शून्यक देते हैं। टिप: मूल बिंदु भी शून्यक दे सकता है।
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किसी घन बहुपद का आलेख (x)-अक्ष को तीन अलग-अलग बिंदुओं पर काटता है। वास्तविक शून्यकों की संख्या क्या है?
The graph of a cubic polynomial cuts the (x)-axis at three distinct points. What is the number of real zeroes?
#cubic graph zeroes
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A तीन / Three
B दो / Two
C एक / One
D शून्य / Zero
Explanation opens after your attempt
Correct Answer
A. तीन / Three
Step 1
Concept
Three intersection points show three real zeroes. Tip: count each distinct (x)-axis intersection.
Step 2
Why this answer is correct
The correct answer is A. तीन / Three. Three intersection points show three real zeroes. Tip: count each distinct (x)-axis intersection.
Step 3
Exam Tip
तीन कटान बिंदु तीन वास्तविक शून्यक बताते हैं। टिप: प्रत्येक अलग (x)-अक्ष कटान को गिनें।
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शून्य बहुपद (p(x)=0) का हर (x)-मान क्या कहलाता है?
For the zero polynomial (p(x)=0) what is every (x)-value called?
#zero polynomial concept
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A शून्यक / Zero
B केवल धनात्मक संख्या / Only positive number
C केवल ऋणात्मक संख्या / Only negative number
D कोई शून्यक नहीं / No zero
Explanation opens after your attempt
Correct Answer
A. शून्यक / Zero
Step 1
Concept
For the zero polynomial the value is (0) for every (x). Tip: this is a special case.
Step 2
Why this answer is correct
The correct answer is A. शून्यक / Zero. For the zero polynomial the value is (0) for every (x). Tip: this is a special case.
Step 3
Exam Tip
शून्य बहुपद में हर (x) पर मान (0) होता है। टिप: यह विशेष स्थिति है।
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अशून्य स्थिर बहुपद (p(x)=5) के आलेख का (x)-अक्ष से संबंध क्या है?
What is the relation of the graph of the non-zero constant polynomial (p(x)=5) with the (x)-axis?
#constant polynomial graph
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A यह (x)-अक्ष के समांतर है और उसे नहीं काटता / It is parallel to the (x)-axis and does not cut it
B यह (x)-अक्ष को दो बार काटता है / It cuts the (x)-axis twice
C यह मूल बिंदु से गुजरता है / It passes through the origin
D यह (y)-अक्ष के समांतर है / It is parallel to the (y)-axis
Explanation opens after your attempt
Correct Answer
A. यह (x)-अक्ष के समांतर है और उसे नहीं काटता / It is parallel to the (x)-axis and does not cut it
Step 1
Concept
The value (p(x)=5) is never (0) so it has no zero. Tip: a non-zero constant polynomial has no zero.
Step 2
Why this answer is correct
The correct answer is A. यह (x)-अक्ष के समांतर है और उसे नहीं काटता / It is parallel to the (x)-axis and does not cut it. The value (p(x)=5) is never (0) so it has no zero. Tip: a non-zero constant polynomial has no zero.
Step 3
Exam Tip
(p(x)=5) कभी (0) नहीं होता इसलिए शून्यक नहीं है। टिप: अशून्य स्थिर बहुपद का शून्यक नहीं होता।
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बहुपद (p(x)=3x) के आलेख का (x)-अक्ष कटान कौन सा है?
What is the (x)-axis intersection of the graph of (p(x)=3x)?
#linear through origin
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A ((0,0))
B ((3,0))
C ((0,3))
D ((-3,0))
Explanation opens after your attempt
Correct Answer
A. ((0,0))
Step 1
Concept
From (3x=0) we get (x=0). Tip: the coefficient does not change the zero in this case.
Step 2
Why this answer is correct
The correct answer is A. ((0,0)). From (3x=0) we get (x=0). Tip: the coefficient does not change the zero in this case.
Step 3
Exam Tip
(3x=0) से (x=0) मिलता है। टिप: गुणांक बदलने से इस स्थिति में शून्यक नहीं बदलता।
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यदि रेखा (y=x+2) (x)-अक्ष को काटती है तो कटान का (x)-मान क्या है?
If the line (y=x+2) cuts the (x)-axis then what is the (x)-value of the intersection?
#line x intercept
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A (-2)
B (2)
C (0)
D (1)
Explanation opens after your attempt
Step 1
Concept
Put (y=0) on the (x)-axis to get (x+2=0). Tip: setting (y=0) is the easiest method.
Step 2
Why this answer is correct
The correct answer is A. (-2). Put (y=0) on the (x)-axis to get (x+2=0). Tip: setting (y=0) is the easiest method.
Step 3
Exam Tip
(x)-अक्ष पर (y=0) रखकर (x+2=0) मिलता है। टिप: (y=0) रखना सबसे आसान तरीका है।
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यदि रेखा (y=5-x) का आलेख दिया हो तो शून्यक क्या होगा?
If the graph of the line (y=5-x) is given then what is the zero?
#linear equation graph
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A (5)
B (-5)
C (0)
D (1)
Explanation opens after your attempt
Step 1
Concept
From (5-x=0) we get (x=5). Tip: take (y) as (0) for the zero.
Step 2
Why this answer is correct
The correct answer is A. (5). From (5-x=0) we get (x=5). Tip: take (y) as (0) for the zero.
Step 3
Exam Tip
(5-x=0) से (x=5) मिलता है। टिप: शून्यक के लिए (y) को (0) मानें।
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आलेख में (x)-अक्ष पर केवल बिंदु ((8,0)) दिख रहा है। बहुपद के वास्तविक शून्यक की संख्या क्या है?
Only the point ((8,0)) is visible on the (x)-axis in the graph. What is the number of real zeroes of the polynomial?
#count intersections
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A एक / One
B आठ / Eight
C शून्य / Zero
D दो / Two
Explanation opens after your attempt
Step 1
Concept
Only one (x)-axis intersection is visible so there is one real zero. Tip: the count comes from the number of points.
Step 2
Why this answer is correct
The correct answer is A. एक / One. Only one (x)-axis intersection is visible so there is one real zero. Tip: the count comes from the number of points.
Step 3
Exam Tip
केवल एक (x)-अक्ष कटान दिख रहा है इसलिए एक वास्तविक शून्यक है। टिप: संख्या बिंदुओं की गिनती से आती है।
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यदि बहुपद के आलेख का (x)-अक्ष से कटान ((a,0)) है तो शून्यक क्या होगा?
If the (x)-axis intersection of a polynomial graph is ((a,0)) then what is the zero?
#general intercept rule
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A (a)
B (0)
C (a+0)
D (-a)
Explanation opens after your attempt
Step 1
Concept
In the intersection point ((a,0)) the (x)-value (a) is the zero. Tip: take the first value of the ordered pair.
Step 2
Why this answer is correct
The correct answer is A. (a). In the intersection point ((a,0)) the (x)-value (a) is the zero. Tip: take the first value of the ordered pair.
Step 3
Exam Tip
कटान बिंदु ((a,0)) में (x)-मान (a) ही शून्यक है। टिप: क्रमित युग्म का पहला मान लें।
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यदि (p(2)=3) है तो बिंदु ((2,3)) आलेख पर है। क्या (2) शून्यक है?
If (p(2)=3) then the point ((2,3)) is on the graph. Is (2) a zero?
#not a zero value
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A नहीं / No
B हाँ / Yes
C केवल द्विघात में हाँ / Yes only in quadratic
D निर्धारित नहीं किया जा सकता / Cannot be decided
Explanation opens after your attempt
Correct Answer
A. नहीं / No
Step 1
Concept
For a zero (p(2)) should be (0). Tip: if (p(a)\neq0) then (a) is not a zero.
Step 2
Why this answer is correct
The correct answer is A. नहीं / No. For a zero (p(2)) should be (0). Tip: if (p(a)\neq0) then (a) is not a zero.
Step 3
Exam Tip
शून्यक के लिए (p(2)) को (0) होना चाहिए था। टिप: (p(a)\neq0) हो तो (a) शून्यक नहीं है।
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यदि (p(-4)=0) है तो आलेख किस बिंदु से अवश्य गुजरेगा?
If (p(-4)=0) then through which point must the graph pass?
#function to point
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A ((-4,0))
B ((0,-4))
C ((4,0))
D ((-4,-4))
Explanation opens after your attempt
Correct Answer
A. ((-4,0))
Step 1
Concept
The value (p(-4)=0) gives the point ((-4,0)). Tip: treat (p(x)) as the (y)-coordinate.
Step 2
Why this answer is correct
The correct answer is A. ((-4,0)). The value (p(-4)=0) gives the point ((-4,0)). Tip: treat (p(x)) as the (y)-coordinate.
Step 3
Exam Tip
(p(-4)=0) बिंदु ((-4,0)) देता है। टिप: (p(x)) को (y)-निर्देशांक समझें।
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कौन सा बिंदु किसी बहुपद के शून्यक को सीधे दिखाता है?
Which point directly shows a zero of a polynomial?
#identify zero point
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A ((9,0))
B ((0,9))
C ((9,9))
D ((0,-9))
Explanation opens after your attempt
Correct Answer
A. ((9,0))
Step 1
Concept
A point showing a zero has (y)-coordinate (0). Tip: choose points lying on the (x)-axis.
Step 2
Why this answer is correct
The correct answer is A. ((9,0)). A point showing a zero has (y)-coordinate (0). Tip: choose points lying on the (x)-axis.
Step 3
Exam Tip
शून्यक वाले बिंदु का (y)-निर्देशांक (0) होता है। टिप: (x)-अक्ष पर पड़े बिंदु चुनें।
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आलेख (x)-अक्ष को ((-1,0)) और ((1,0)) पर काटता है। शून्यकों का योग क्या है?
The graph cuts the (x)-axis at ((-1,0)) and ((1,0)). What is the sum of zeroes?
#symmetric zeroes
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A (0)
B (2)
C (-2)
D (1)
Explanation opens after your attempt
Step 1
Concept
The zeroes are (-1) and (1) and their sum is (0). Tip: symmetric intersections often give sum (0).
Step 2
Why this answer is correct
The correct answer is A. (0). The zeroes are (-1) and (1) and their sum is (0). Tip: symmetric intersections often give sum (0).
Step 3
Exam Tip
शून्यक (-1) और (1) हैं जिनका योग (0) है। टिप: सममित कटान अक्सर योग (0) देते हैं।
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यदि परवलय (x)-अक्ष को ((0,0)) और ((6,0)) पर काटता है तो शून्यकों का गुणनफल क्या है?
If a parabola cuts the (x)-axis at ((0,0)) and ((6,0)) then what is the product of zeroes?
#zero product graph
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A (0)
B (6)
C (-6)
D (36)
Explanation opens after your attempt
Step 1
Concept
The zeroes are (0) and (6) so the product is (0). Tip: any number multiplied by (0) gives (0).
Step 2
Why this answer is correct
The correct answer is A. (0). The zeroes are (0) and (6) so the product is (0). Tip: any number multiplied by (0) gives (0).
Step 3
Exam Tip
शून्यक (0) और (6) हैं इसलिए गुणनफल (0) है। टिप: किसी भी संख्या से (0) गुणा करने पर (0) मिलता है।
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किस आलेख से दो वास्तविक शून्यक मिलेंगे?
Which graph will give two real zeroes?
#two real zeroes
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A जो (x)-अक्ष को दो अलग बिंदुओं पर काटे / One that cuts the (x)-axis at two distinct points
B जो (y)-अक्ष को दो बार काटे / One that cuts the (y)-axis twice
C जो (x)-अक्ष के समांतर हो / One that is parallel to the (x)-axis
D जो केवल (y)-अक्ष को छुए / One that only touches the (y)-axis
Explanation opens after your attempt
Correct Answer
A. जो (x)-अक्ष को दो अलग बिंदुओं पर काटे / One that cuts the (x)-axis at two distinct points
Step 1
Concept
Two real zeroes need two distinct (x)-axis intersections. Tip: (y)-axis intersections do not count as zeroes.
Step 2
Why this answer is correct
The correct answer is A. जो (x)-अक्ष को दो अलग बिंदुओं पर काटे / One that cuts the (x)-axis at two distinct points. Two real zeroes need two distinct (x)-axis intersections. Tip: (y)-axis intersections do not count as zeroes.
Step 3
Exam Tip
दो वास्तविक शून्यक के लिए दो अलग (x)-अक्ष कटान चाहिए। टिप: (y)-अक्ष कटान शून्यक नहीं गिनाता।
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किस स्थिति में बहुपद का (3) शून्यक होगा?
In which situation will (3) be a zero of the polynomial?
#identify given zero
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A आलेख ((3,0)) से गुजरे / The graph passes through ((3,0))
B आलेख ((0,3)) से गुजरे / The graph passes through ((0,3))
C आलेख ((3,3)) से गुजरे / The graph passes through ((3,3))
D आलेख ((-3,0)) से गुजरे / The graph passes through ((-3,0))
Explanation opens after your attempt
Correct Answer
A. आलेख ((3,0)) से गुजरे / The graph passes through ((3,0))
Step 1
Concept
If (3) is a zero then (p(3)=0). Tip: look for the point ((3,0)).
Step 2
Why this answer is correct
The correct answer is A. आलेख ((3,0)) से गुजरे / The graph passes through ((3,0)). If (3) is a zero then (p(3)=0). Tip: look for the point ((3,0)).
Step 3
Exam Tip
(3) शून्यक होने पर (p(3)=0) होता है। टिप: बिंदु ((3,0)) खोजें।
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किस स्थिति में (-6) बहुपद का शून्यक होगा?
In which situation will (-6) be a zero of the polynomial?
#negative zero identify
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A आलेख ((-6,0)) पर (x)-अक्ष को काटे / The graph cuts the (x)-axis at ((-6,0))
B आलेख ((0,-6)) पर (y)-अक्ष को काटे / The graph cuts the (y)-axis at ((0,-6))
C आलेख ((6,0)) पर (x)-अक्ष को काटे / The graph cuts the (x)-axis at ((6,0))
D आलेख ((-6,6)) से गुजरे / The graph passes through ((-6,6))
Explanation opens after your attempt
Correct Answer
A. आलेख ((-6,0)) पर (x)-अक्ष को काटे / The graph cuts the (x)-axis at ((-6,0))
Step 1
Concept
For (-6) to be a zero (p(-6)=0). Tip: do not miss the negative sign.
Step 2
Why this answer is correct
The correct answer is A. आलेख ((-6,0)) पर (x)-अक्ष को काटे / The graph cuts the (x)-axis at ((-6,0)). For (-6) to be a zero (p(-6)=0). Tip: do not miss the negative sign.
Step 3
Exam Tip
(-6) शून्यक होने का अर्थ (p(-6)=0) है। टिप: ऋण चिह्न को न छोड़ें।
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यदि किसी बहुपद के आलेख का कोई भी बिंदु (x)-अक्ष पर नहीं है तो कौन सा कथन सही है?
If no point of a polynomial graph lies on the (x)-axis then which statement is correct?
#no x axis point
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A उसका कोई वास्तविक शून्यक नहीं है / It has no real zero
B उसका एक वास्तविक शून्यक है / It has one real zero
C उसके दो वास्तविक शून्यक हैं / It has two real zeroes
D हर संख्या शून्यक है / Every number is a zero
Explanation opens after your attempt
Correct Answer
A. उसका कोई वास्तविक शून्यक नहीं है / It has no real zero
Step 1
Concept
A real zero appears only on the (x)-axis. Tip: check meeting the (x)-axis not distance from it.
Step 2
Why this answer is correct
The correct answer is A. उसका कोई वास्तविक शून्यक नहीं है / It has no real zero. A real zero appears only on the (x)-axis. Tip: check meeting the (x)-axis not distance from it.
Step 3
Exam Tip
वास्तविक शून्यक (x)-अक्ष पर ही दिखता है। टिप: (x)-अक्ष से दूरी नहीं बल्कि मिलना देखें।
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किसी बहुपद का आलेख (x)-अक्ष को (x=10) पर काटता है। कौन सा कथन सही है?
A polynomial graph cuts the (x)-axis at (x=10). Which statement is correct?
#x value zero
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A (p(10)=0)
B (p(0)=10)
C (p(10)=10)
D (p(-10)=0)
Explanation opens after your attempt
Correct Answer
A. (p(10)=0)
Step 1
Concept
An (x)-axis cut at (x=10) means (y=0). Tip: on the (x)-axis the function value is (0).
Step 2
Why this answer is correct
The correct answer is A. (p(10)=0). An (x)-axis cut at (x=10) means (y=0). Tip: on the (x)-axis the function value is (0).
Step 3
Exam Tip
(x=10) पर (x)-अक्ष कटान का अर्थ (y=0) है। टिप: (x)-अक्ष पर फलन मान (0) होता है।
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यदि (p(5)=0) और (p(-2)=0) है तो आलेख (x)-अक्ष को किन (x)-मानों पर काटेगा?
If (p(5)=0) and (p(-2)=0) then at which (x)-values will the graph cut the (x)-axis?
#two values zero
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A (5) और (-2) / (5) and (-2)
B (0) और (5) / (0) and (5)
C (2) और (-5) / (2) and (-5)
D (5) और (2) / (5) and (2)
Explanation opens after your attempt
Correct Answer
A. (5) और (-2) / (5) and (-2)
Step 1
Concept
The (x)-values where (p(x)=0) give the intersections. Tip: read (p(a)=0) directly as an (x=a) cut.
Step 2
Why this answer is correct
The correct answer is A. (5) और (-2) / (5) and (-2). The (x)-values where (p(x)=0) give the intersections. Tip: read (p(a)=0) directly as an (x=a) cut.
Step 3
Exam Tip
जिन (x)-मानों पर (p(x)=0) है वही कटान देते हैं। टिप: (p(a)=0) को सीधे (x=a) कटान मानें।
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एक विद्यार्थी ने ((0,7)) को देखकर (7) को शून्यक कहा। गलती क्या है?
A student saw ((0,7)) and called (7) a zero. What is the mistake?
#common mistake graph
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A यह (y)-अक्ष कटान है और \(y\neq0\) है / It is a (y)-axis intercept and \(y\neq0\)
B (7) हमेशा शून्यक होता है / (7) is always a zero
C हर (y)-अक्ष कटान शून्यक है / Every (y)-axis intercept is a zero
D बिंदु में कोई जानकारी नहीं है / The point has no information
Explanation opens after your attempt
Correct Answer
A. यह (y)-अक्ष कटान है और \(y\neq0\) है / It is a (y)-axis intercept and \(y\neq0\)
Step 1
Concept
For a zero the point must lie on the (x)-axis. Tip: check that the second coordinate is (0).
Step 2
Why this answer is correct
The correct answer is A. यह (y)-अक्ष कटान है और \(y\neq0\) है / It is a (y)-axis intercept and \(y\neq0\). For a zero the point must lie on the (x)-axis. Tip: check that the second coordinate is (0).
Step 3
Exam Tip
शून्यक के लिए बिंदु (x)-अक्ष पर होना चाहिए। टिप: दूसरे निर्देशांक को (0) जांचें।
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परवलय (x)-अक्ष को ((2,0)) और ((2,0)) पर ही छूता है। अलग वास्तविक शून्यकों की संख्या क्या है?
A parabola touches the (x)-axis only at ((2,0)). What is the number of distinct real zeroes?
#repeated zero graph
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A एक / One
B दो / Two
C शून्य / Zero
D चार / Four
Explanation opens after your attempt
Step 1
Concept
For a repeated zero the only distinct (x)-value is (2). Tip: do not count the same point twice for distinct zeroes.
Step 2
Why this answer is correct
The correct answer is A. एक / One. For a repeated zero the only distinct (x)-value is (2). Tip: do not count the same point twice for distinct zeroes.
Step 3
Exam Tip
दोहराया शून्यक होने पर अलग (x)-मान केवल (2) है। टिप: अलग शून्यक गिनते समय समान बिंदु दो बार न गिनें।
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यदि आलेख ((1,0)), ((4,0)) और ((0,6)) से गुजरता है तो शून्यक कौन से हैं?
If a graph passes through ((1,0)), ((4,0)) and ((0,6)) then what are the zeroes?
#select zero points
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A (1) और (4) / (1) and (4)
B (0) और (6) / (0) and (6)
C (1), (4) और (6) / (1), (4) and (6)
D केवल (6) / Only (6)
Explanation opens after your attempt
Correct Answer
A. (1) और (4) / (1) and (4)
Step 1
Concept
Only the points with (y=0) give zeroes. Tip: treat ((0,6)) as a (y)-axis intercept.
Step 2
Why this answer is correct
The correct answer is A. (1) और (4) / (1) and (4). Only the points with (y=0) give zeroes. Tip: treat ((0,6)) as a (y)-axis intercept.
Step 3
Exam Tip
केवल (y=0) वाले बिंदु शून्यक देते हैं। टिप: ((0,6)) को (y)-अक्ष कटान समझें।
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यदि (x)-अक्ष को काटने वाले बिंदु ((-7,0)) और ((-3,0)) हैं तो बड़ा शून्यक कौन सा है?
If the points cutting the (x)-axis are ((-7,0)) and ((-3,0)) then which is the greater zero?
#compare negative zeroes
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A (-3)
B (-7)
C (0)
D (7)
Explanation opens after your attempt
Step 1
Concept
The zeroes are (-7) and (-3) and (-3) is greater. Tip: the number to the right on the number line is greater.
Step 2
Why this answer is correct
The correct answer is A. (-3). The zeroes are (-7) and (-3) and (-3) is greater. Tip: the number to the right on the number line is greater.
Step 3
Exam Tip
शून्यक (-7) और (-3) हैं और (-3) बड़ा है। टिप: संख्या रेखा पर दाईं ओर वाली संख्या बड़ी होती है।
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यदि बहुपद (p(x)=x-2 -9) का आलेख बनाया जाए तो (x)-अक्ष कटान कौन से होंगे?
If the graph of (p(x)=x-2 -9) is drawn then what will be the (x)-axis intersections?
#quadratic simple zeroes
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A ((-3,0)) और ((3,0)) / ((-3,0)) and ((3,0))
B ((0,-9)) और ((9,0)) / ((0,-9)) and ((9,0))
C ((3,3)) और ((-3,-3)) / ((3,3)) and ((-3,-3))
D कोई नहीं / None
Explanation opens after your attempt
Correct Answer
A. ((-3,0)) और ((3,0)) / ((-3,0)) and ((3,0))
Step 1
Concept
Solving \(x^2-9=0\) gives \(x=\pm3\). Tip: recognize \(a^2-b^2\).
Step 2
Why this answer is correct
The correct answer is A. ((-3,0)) और ((3,0)) / ((-3,0)) and ((3,0)). Solving \(x^2-9=0\) gives \(x=\pm3\). Tip: recognize \(a^2-b^2\).
Step 3
Exam Tip
\(x^2-9=0\) से \(x=\pm3\) मिलता है। टिप: \(a^2-b^2\) को पहचानें।
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बहुपद (p(x)=x-2 ) का आलेख (x)-अक्ष से कैसे मिलता है?
How does the graph of (p(x)=x-2 ) meet the (x)-axis?
#x square graph
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A मूल बिंदु पर स्पर्श करता है / It touches at the origin
B दो अलग बिंदुओं पर काटता है / It cuts at two distinct points
C कहीं नहीं मिलता / It does not meet anywhere
D (x=1) पर काटता है / It cuts at (x=1)
Explanation opens after your attempt
Correct Answer
A. मूल बिंदु पर स्पर्श करता है / It touches at the origin
Step 1
Concept
From \(x^2=0\) only (x=0) is obtained. Tip: this is a repeated zero.
Step 2
Why this answer is correct
The correct answer is A. मूल बिंदु पर स्पर्श करता है / It touches at the origin. From \(x^2=0\) only (x=0) is obtained. Tip: this is a repeated zero.
Step 3
Exam Tip
\(x^2=0\) से केवल (x=0) मिलता है। टिप: यह एक दोहराया शून्यक है।
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यदि बहुपद (p(x)=(x-2)(x+5)) है तो आलेख (x)-अक्ष को कहाँ काटेगा?
If the polynomial is (p(x)=(x-2)(x+5)) then where will the graph cut the (x)-axis?
#factor zero graph
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A ((2,0)) और ((-5,0)) / ((2,0)) and ((-5,0))
B ((-2,0)) और ((5,0)) / ((-2,0)) and ((5,0))
C ((0,2)) और ((0,-5)) / ((0,2)) and ((0,-5))
D ((2,5)) और ((-5,2)) / ((2,5)) and ((-5,2))
Explanation opens after your attempt
Correct Answer
A. ((2,0)) और ((-5,0)) / ((2,0)) and ((-5,0))
Step 1
Concept
Making each factor zero gives (x=2) and (x=-5). Tip: set each factor equal to (0).
Step 2
Why this answer is correct
The correct answer is A. ((2,0)) और ((-5,0)) / ((2,0)) and ((-5,0)). Making each factor zero gives (x=2) and (x=-5). Tip: set each factor equal to (0).
Step 3
Exam Tip
कारक शून्य करने पर (x=2) और (x=-5) मिलते हैं। टिप: हर कारक को अलग से (0) रखें।
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किसी बहुपद के ग्राफ में (x)-अक्ष कटान की गिनती का मुख्य उपयोग क्या है?
What is the main use of counting (x)-axis intersections in a polynomial graph?
#graph interpretation use
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A वास्तविक शून्यकों की संख्या जानना / To know the number of real zeroes
B घात हमेशा जानना / To always know the degree
C स्थिर पद तुरंत जानना / To know the constant term immediately
D रंग तय करना / To decide the color
Explanation opens after your attempt
Correct Answer
A. वास्तविक शून्यकों की संख्या जानना / To know the number of real zeroes
Step 1
Concept
The (x)-axis intersections tell the number of real zeroes. Tip: first count intersections from the graph.
Step 2
Why this answer is correct
The correct answer is A. वास्तविक शून्यकों की संख्या जानना / To know the number of real zeroes. The (x)-axis intersections tell the number of real zeroes. Tip: first count intersections from the graph.
Step 3
Exam Tip
(x)-अक्ष कटान वास्तविक शून्यकों की संख्या बताते हैं। टिप: ग्राफ से पहले कटान गिनें।
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यदि किसी बहुपद के आलेख का (x)-अक्ष से केवल एक कटान (x=-8) पर है तो कौन सा कथन सही है?
If a polynomial graph has only one (x)-axis intersection at (x=-8) then which statement is correct?
#single negative intercept
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A उसका एक वास्तविक शून्यक (-8) है / It has one real zero (-8)
B उसके आठ वास्तविक शून्यक हैं / It has eight real zeroes
C उसका शून्यक (8) है / Its zero is (8)
D उसका कोई वास्तविक शून्यक नहीं है / It has no real zero
Explanation opens after your attempt
Correct Answer
A. उसका एक वास्तविक शून्यक (-8) है / It has one real zero (-8)
Step 1
Concept
There is only one intersection and its (x)-value is (-8). Tip: check both the count and the (x)-value.
Step 2
Why this answer is correct
The correct answer is A. उसका एक वास्तविक शून्यक (-8) है / It has one real zero (-8). There is only one intersection and its (x)-value is (-8). Tip: check both the count and the (x)-value.
Step 3
Exam Tip
केवल एक कटान है और उसका (x)-मान (-8) है। टिप: कटान की संख्या और (x)-मान दोनों देखें।
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