Question 1/10
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि किसी ग्राफ के लिए (p(-3)<0), (p(1)=0), और (p(4)>0) है तो निश्चित शून्यक कौन सा है?
If for a graph (p(-3)<0), (p(1)=0), and (p(4)>0), which zero is certain?
#function-values
#zero-identification
#reasoning
A (1)
B (-3)
C (4)
D (-3) और (4) / (-3) and (4)
Explanation opens after your attempt
Step 1
Concept
Only (p(1)=0) directly gives a zero. Positive or negative values are not zeroes.
Step 2
Why this answer is correct
The correct answer is A. (1). Only (p(1)=0) directly gives a zero. Positive or negative values are not zeroes.
Step 3
Exam Tip
केवल (p(1)=0) सीधे शून्यक बताता है। धनात्मक या ऋणात्मक मान शून्यक नहीं होते।
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Question 2/10
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(-7)=0), (p(-3)<0), (p(4)=0), (p(8)>0) है, तो दिए गए शून्यकों के बीच दूरी क्या है?
If (p(-7)=0), (p(-3)<0), (p(4)=0), (p(8)>0), what is the distance between the given zeroes?
#function values
#distance
#zeroes
A (11)
B (3)
C (15)
D (-11)
Explanation opens after your attempt
Step 1
Concept
The given zeroes are (-7) and (4), so the distance is (4-(-7)=11). Tip: take only (x)-values where (p(x)=0).
Step 2
Why this answer is correct
The correct answer is A. (11). The given zeroes are (-7) and (4), so the distance is (4-(-7)=11). Tip: take only (x)-values where (p(x)=0).
Step 3
Exam Tip
दिए गए शून्यक (-7) और (4) हैं इसलिए दूरी (4-(-7)=11) है। टिप: केवल (p(x)=0) वाले (x)-मान लें।
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Question 3/10
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि (p(-6)=0), (p(-2)<0), (p(5)=0), (p(9)>0) है, तो दिए गए शून्यकों के बीच दूरी क्या है?
If (p(-6)=0), (p(-2)<0), (p(5)=0), (p(9)>0), what is the distance between the given zeroes?
#function values
#distance
#zeroes
A (1)
B (11)
C (14)
D (-11)
Explanation opens after your attempt
Step 1
Concept
The given zeroes are (-6) and (5), so the distance is (5-(-6)=11). Tip: take only (x)-values where (p(x)=0).
Step 2
Why this answer is correct
The correct answer is B. (11). The given zeroes are (-6) and (5), so the distance is (5-(-6)=11). Tip: take only (x)-values where (p(x)=0).
Step 3
Exam Tip
दिए गए शून्यक (-6) और (5) हैं, इसलिए दूरी (5-(-6)=11) है। टिप: केवल (p(x)=0) वाले (x)-मान लें।
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Question 4/10
Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि (p(-8)=0), (p(-2)>0), (p(3)=0) और (p(9)<0) है तो दिए गए शून्यकों का योग क्या है?
If (p(-8)=0), (p(-2)>0), (p(3)=0) and (p(9)<0), what is the sum of the given zeroes?
#function values
#sum of zeroes
#graph
A (-5)
B (5)
C (-11)
D (0)
Explanation opens after your attempt
Step 1
Concept
The given zeroes are (-8) and (3), so their sum is (-5). Tip: take only the (x)-values where (p(x)=0).
Step 2
Why this answer is correct
The correct answer is A. (-5). The given zeroes are (-8) and (3), so their sum is (-5). Tip: take only the (x)-values where (p(x)=0).
Step 3
Exam Tip
दिए गए शून्यक (-8) और (3) हैं इसलिए योग (-5) है। टिप: केवल (p(x)=0) वाले (x)-मान लें।
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Question 5/10
Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(-6)=0), (p(-1)>0), (p(4)=0) और (p(7)<0) है, तो दिए गए शून्यकों का गुणनफल क्या है?
If (p(-6)=0), (p(-1)>0), (p(4)=0) and (p(7)<0), what is the product of the given zeroes?
#function values
#product of zeroes
#graph
A (-24)
B (24)
C (-7)
D (0)
Explanation opens after your attempt
Step 1
Concept
The given zeroes are (-6) and (4), so the product is (-24). Tip: take only (x)-values where (p(x)=0).
Step 2
Why this answer is correct
The correct answer is A. (-24). The given zeroes are (-6) and (4), so the product is (-24). Tip: take only (x)-values where (p(x)=0).
Step 3
Exam Tip
दिए गए शून्यक (-6) और (4) हैं, इसलिए गुणनफल (-24) है। टिप: केवल (p(x)=0) वाले (x)-मान लें।
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Question 6/10
Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
एक बहुपद का ग्राफ (x)-अक्ष को नहीं काटता, पर (p(1)=4) और (p(3)=9) हैं। सही निष्कर्ष क्या है?
A polynomial graph does not cut the (x)-axis, but (p(1)=4) and (p(3)=9). What is the correct conclusion?
#no real zero
#function values
#graph
A (1) और (3) शून्यक हैं / (1) and (3) are zeroes
B केवल (4) शून्यक है / Only (4) is a zero
C कोई वास्तविक शून्यक नहीं है / There is no real zero
D दो वास्तविक शून्यक हैं / There are two real zeroes
Explanation opens after your attempt
Correct Answer
C. कोई वास्तविक शून्यक नहीं है / There is no real zero
Step 1
Concept
The graph does not meet the (x)-axis and the given values are not zero. Tip: do not call a value a zero unless the function value is (0).
Step 2
Why this answer is correct
The correct answer is C. कोई वास्तविक शून्यक नहीं है / There is no real zero. The graph does not meet the (x)-axis and the given values are not zero. Tip: do not call a value a zero unless the function value is (0).
Step 3
Exam Tip
ग्राफ (x)-अक्ष से नहीं मिलता और दिए गए मान भी शून्य नहीं हैं। टिप: फलन मान (0) न हो तो शून्यक न मानें।
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Question 7/10
Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि (p(0)=0) और (p(5)=0), तो ग्राफ के बारे में कौन सा कथन सही है?
If (p(0)=0) and (p(5)=0), which statement about the graph is correct?
#origin
#zeroes
#function values
A ग्राफ ((0,0)) और ((5,0)) से गुजरता है / The graph passes through ((0,0)) and ((5,0))
B ग्राफ ((0,5)) और ((5,5)) से गुजरता है / The graph passes through ((0,5)) and ((5,5))
C ग्राफ (x)-अक्ष को नहीं काटता / The graph does not cut the (x)-axis
D ग्राफ केवल (y)-अक्ष को काटता है / The graph cuts only the (y)-axis
Explanation opens after your attempt
Correct Answer
A. ग्राफ ((0,0)) और ((5,0)) से गुजरता है / The graph passes through ((0,0)) and ((5,0))
Step 1
Concept
At both given (x)-values, the function value is (0). Tip: when (p(0)=0), the graph passes through the origin.
Step 2
Why this answer is correct
The correct answer is A. ग्राफ ((0,0)) और ((5,0)) से गुजरता है / The graph passes through ((0,0)) and ((5,0)). At both given (x)-values, the function value is (0). Tip: when (p(0)=0), the graph passes through the origin.
Step 3
Exam Tip
दोनों दिए गए (x)-मानों पर फलन मान (0) है। टिप: (p(0)=0) होने पर ग्राफ मूल बिंदु से गुजरता है।
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Question 8/10
Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि द्विघात बहुपद का ग्राफ (x)-अक्ष को ((-2,0)) और ((7,0)) पर काटता है, तो (p(-2)) और (p(7)) के मान क्या होंगे?
If the graph of a quadratic polynomial cuts the (x)-axis at ((-2,0)) and ((7,0)), what will be the values of (p(-2)) and (p(7))?
#function values
#intercepts
#quadratic
A दोनों (0) / Both (0)
B दोनों धनात्मक / Both positive
C दोनों ऋणात्मक / Both negative
D एक (0) और दूसरा (7) / One is (0) and the other is (7)
Explanation opens after your attempt
Correct Answer
A. दोनों (0) / Both (0)
Step 1
Concept
At an (x)-axis intersection, (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. दोनों (0) / Both (0). At an (x)-axis intersection, (y=p(x)=0). Tip: read the function value directly from the intersection point.
Step 3
Exam Tip
(x)-अक्ष कटान पर (y=p(x)=0) होता है। टिप: कटान बिंदु से फलन मान सीधे पढ़ें।
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Question 9/10
Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि (p(-3)=0), (p(0)=5) और (p(4)=0), तो ग्राफ (x)-अक्ष को किन बिंदुओं पर काटेगा?
If (p(-3)=0), (p(0)=5) and (p(4)=0), at which points will the graph cut the (x)-axis?
#function values
#intercepts
#zeroes
A ((0,5)) और ((4,0)) / ((0,5)) and ((4,0))
B ((-3,0)) और ((4,0)) / ((-3,0)) and ((4,0))
C ((-3,5)) और ((0,4)) / ((-3,5)) and ((0,4))
D ((0,0)) और ((5,0)) / ((0,0)) and ((5,0))
Explanation opens after your attempt
Correct Answer
B. ((-3,0)) और ((4,0)) / ((-3,0)) and ((4,0))
Step 1
Concept
Where (p(x)=0), there is an (x)-axis intersection. Tip: (p(0)=5) does not give a zero.
Step 2
Why this answer is correct
The correct answer is B. ((-3,0)) और ((4,0)) / ((-3,0)) and ((4,0)). Where (p(x)=0), there is an (x)-axis intersection. Tip: (p(0)=5) does not give a zero.
Step 3
Exam Tip
जहाँ (p(x)=0) है वहीं (x)-अक्ष कटान है। टिप: (p(0)=5) शून्यक नहीं देता।
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Question 10/10
Easy Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
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
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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