Question 1/30
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि ग्राफ (x)-अक्ष को (a) और (b) पर काटता है जहाँ \(a\neq b\) है तो (p(a)) और (p(b)) के मान क्या होंगे?
If a graph cuts the (x)-axis at (a) and (b) where \(a\neq b\), what are the values of (p(a)) and (p(b))?
#symbolic-zeroes
#x-axis
#reasoning
A दोनों (0) / Both are (0)
B दोनों (1) / Both are (1)
C एक (0) और एक (1) / One is (0) and one is (1)
D दोनों बराबर नहीं / They are not equal
Explanation opens after your attempt
Correct Answer
A. दोनों (0) / Both are (0)
Step 1
Concept
Meeting the (x)-axis means the polynomial value is (0). Hence (p(x)=0) at both places.
Step 2
Why this answer is correct
The correct answer is A. दोनों (0) / Both are (0). Meeting the (x)-axis means the polynomial value is (0). Hence (p(x)=0) at both places.
Step 3
Exam Tip
(x)-अक्ष पर मिलने का अर्थ बहुपद का मान (0) है। इसलिए दोनों स्थानों पर (p(x)=0) होगा।
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Question 2/30
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
किसी बहुपद का ग्राफ (x)-अक्ष से ((7,0)) पर मिलता है। उस बिंदु पर (p(x)) का मान क्या होगा?
A polynomial graph meets the (x)-axis at ((7,0)). What is the value of (p(x)) at that point?
#x-axis
#function-value
#zero
A (0)
B (7)
C (-7)
D (1)
Explanation opens after your attempt
Step 1
Concept
Every point on the (x)-axis has (y=0). Therefore (p(7)=0).
Step 2
Why this answer is correct
The correct answer is A. (0). Every point on the (x)-axis has (y=0). Therefore (p(7)=0).
Step 3
Exam Tip
(x)-अक्ष पर हर बिंदु का (y)-मान (0) होता है। इसलिए (p(7)=0) होगा।
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Question 3/30
Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
किसी बहुपद का ग्राफ (x)-अक्ष को दो बार काटता है और (y)-अक्ष को एक बार काटता है। वास्तविक शून्यक कितने हैं?
A polynomial graph cuts the (x)-axis twice and the (y)-axis once. How many real zeroes does it have?
#x axis
#y axis
#zero count
A एक / One
B दो / Two
C तीन / Three
D निर्धारित नहीं / Not determined
Explanation opens after your attempt
Step 1
Concept
Real zeroes are counted only from (x)-axis intersections. Tip: do not add the (y)-axis intercept to zeroes.
Step 2
Why this answer is correct
The correct answer is B. दो / Two. Real zeroes are counted only from (x)-axis intersections. Tip: do not add the (y)-axis intercept to zeroes.
Step 3
Exam Tip
वास्तविक शून्यक केवल (x)-अक्ष कटान से गिने जाते हैं। टिप: (y)-अक्ष कटान को शून्यक में न जोड़ें।
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Question 4/30
Easy Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
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
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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Question 5/30
Easy Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
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
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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Question 6/30
Easy Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
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
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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Question 7/30
Easy Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
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
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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Question 8/30
Easy Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
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
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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Question 9/30
Easy Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
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
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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Question 10/30
Easy Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
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
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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Question 11/30
Easy Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
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
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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Question 12/30
Easy Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
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
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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Question 13/30
Easy Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
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
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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Question 14/30
Easy Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
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
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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Question 15/30
Easy Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
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
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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Question 16/30
Easy Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
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
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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Question 17/30
Easy Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
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
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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Question 18/30
Easy Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
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
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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Question 19/30
Easy Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
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
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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Question 20/30
Easy Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
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
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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Question 21/30
Easy Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
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
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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Question 22/30
Easy Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
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
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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Question 23/30
Easy Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
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
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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Question 24/30
Easy Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
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
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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Question 25/30
Easy Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
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
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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Question 26/30
Easy Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
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
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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Question 27/30
Easy Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
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
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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Question 28/30
Easy Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
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
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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Question 29/30
Easy Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
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
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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Question 30/30
Easy Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
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
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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