Question 31/40
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
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
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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Question 32/40
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
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
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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Question 33/40
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
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
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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Question 34/40
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
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
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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Question 35/40
Easy Mathematics
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 36/40
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
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
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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Question 37/40
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
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
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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Question 38/40
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
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
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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Question 39/40
Easy Mathematics
Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
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
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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Question 40/40
Easy Mathematics
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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