Question 1/115
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
ग्राफ (x)-अक्ष को काटता नहीं बल्कि (y=2) रेखा को दो बार काटता है। शून्यकों के बारे में क्या निश्चित है?
The graph does not cut the (x)-axis but cuts the line (y=2) twice. What is certain about zeroes?
#horizontal-line
#common-mistake
#zeroes
A दिए गए आधार पर कोई शून्यक नहीं दिखता / No zero is shown from the given data
B दो शून्यक हैं / There are two zeroes
C एक शून्यक है / There is one zero
D अनंत शून्यक हैं / There are infinitely many zeroes
Explanation opens after your attempt
Correct Answer
A. दिए गए आधार पर कोई शून्यक नहीं दिखता / No zero is shown from the given data
Step 1
Concept
Zeroes are linked only with the (x)-axis where (y=0). Intersections with (y=2) do not show zeroes.
Step 2
Why this answer is correct
The correct answer is A. दिए गए आधार पर कोई शून्यक नहीं दिखता / No zero is shown from the given data. Zeroes are linked only with the (x)-axis where (y=0). Intersections with (y=2) do not show zeroes.
Step 3
Exam Tip
शून्यक केवल (x)-अक्ष यानी (y=0) से जुड़े होते हैं। (y=2) से प्रतिच्छेद शून्यक नहीं बताता।
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Question 2/115
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि (p(x)=-(x-3)(x+1)) है तो ग्राफ के शून्यक कौन से हैं?
If (p(x)=-(x-3)(x+1)), what are the zeroes of the graph?
#factor-form
#sign-error
#zeroes
A (3) और (-1) / (3) and (-1)
B (-3) और (1) / (-3) and (1)
C (0) और (-1) / (0) and (-1)
D (3) और (1) / (3) and (1)
Explanation opens after your attempt
Correct Answer
A. (3) और (-1) / (3) and (-1)
Step 1
Concept
The outside negative sign does not change the zeroes. Set the factors equal to zero.
Step 2
Why this answer is correct
The correct answer is A. (3) और (-1) / (3) and (-1). The outside negative sign does not change the zeroes. Set the factors equal to zero.
Step 3
Exam Tip
बाहर का ऋण चिह्न शून्यकों को नहीं बदलता। गुणनखंडों को शून्य रखकर उत्तर निकालें।
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Question 3/115
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
किसी बहुपद के ग्राफ में (y)-अक्ष से प्रतिच्छेद ((0,-8)) है। इससे शून्यक के बारे में कौन सा निष्कर्ष सही है?
A polynomial graph has (y)-intercept ((0,-8)). Which conclusion about zeroes is correct?
#y-intercept
#common-mistake
#zeroes
A इससे शून्यक निश्चित नहीं होता / A zero cannot be determined from this alone
B शून्यक (-8) है / The zero is (-8)
C शून्यक (0) है / The zero is (0)
D शून्यक (8) है / The zero is (8)
Explanation opens after your attempt
Correct Answer
A. इससे शून्यक निश्चित नहीं होता / A zero cannot be determined from this alone
Step 1
Concept
The (y)-intercept tells (p(0)) not all zeroes. Zeroes need (x)-axis intersections.
Step 2
Why this answer is correct
The correct answer is A. इससे शून्यक निश्चित नहीं होता / A zero cannot be determined from this alone. The (y)-intercept tells (p(0)) not all zeroes. Zeroes need (x)-axis intersections.
Step 3
Exam Tip
(y)-प्रतिच्छेद (p(0)) बताता है न कि सभी शून्यक। शून्यक के लिए (x)-अक्ष से प्रतिच्छेद चाहिए।
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Question 4/115
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि किसी द्विघात बहुपद (p(x)) का ग्राफ (x)-अक्ष को (-2) और (5) पर काटता है तो उसके शून्यकों की संख्या क्या है?
If the graph of a quadratic polynomial (p(x)) cuts the (x)-axis at (-2) and (5), how many zeroes does it have?
#polynomials
#zeroes
#graphical-meaning
A दो / Two
B एक / One
C तीन / Three
D कोई नहीं / None
Explanation opens after your attempt
Step 1
Concept
A zero occurs where the graph meets the (x)-axis. In exams count the (x)-intercepts.
Step 2
Why this answer is correct
The correct answer is A. दो / Two. A zero occurs where the graph meets the (x)-axis. In exams count the (x)-intercepts.
Step 3
Exam Tip
ग्राफ जहाँ (x)-अक्ष को काटता है वही शून्यक होता है। परीक्षा में काटने वाले बिंदुओं की संख्या गिनें।
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Question 5/115
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(x)=x-2 -2dx+d-2 -36) है, तो ग्राफ के शून्यक कौन से होंगे?
If (p(x)=x-2 -2dx+d-2 -36), what will be the zeroes of the graph?
#symbolic quadratic
#difference of squares
#zeroes
A (d-6) और (d+6) / (d-6) and (d+6)
B (6-d) और (-d-6) / (6-d) and (-d-6)
C (d) और (36) / (d) and (36)
D कोई नहीं / None
Explanation opens after your attempt
Correct Answer
A. (d-6) और (d+6) / (d-6) and (d+6)
Step 1
Concept
It is ((x-d)2 -36), so \(x-d=\pm6\) and the zeroes are (d-6), (d+6). Tip: use difference of squares.
Step 2
Why this answer is correct
The correct answer is A. (d-6) और (d+6) / (d-6) and (d+6). It is ((x-d)2 -36), so \(x-d=\pm6\) and the zeroes are (d-6), (d+6). Tip: use difference of squares.
Step 3
Exam Tip
यह ((x-d)2 -36) है, इसलिए \(x-d=\pm6\) और शून्यक (d-6), (d+6) हैं। टिप: वर्गों के अंतर का उपयोग करें।
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Question 6/115
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(x)=(x-4)(x-9)(x-15)) है, तो (4<x<9) में ग्राफ कहाँ होगा?
If (p(x)=(x-4)(x-9)(x-15)), where will the graph be for (4<x<9)?
#sign analysis
#cubic graph
#zeroes
A (x)-अक्ष के ऊपर / Above the (x)-axis
B (x)-अक्ष के नीचे / Below the (x)-axis
C ठीक (x)-अक्ष पर / On the (x)-axis
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Correct Answer
A. (x)-अक्ष के ऊपर / Above the (x)-axis
Step 1
Concept
In this interval the signs are (+), (-), (-), so the product is positive. Tip: the product of two negative factors is positive.
Step 2
Why this answer is correct
The correct answer is A. (x)-अक्ष के ऊपर / Above the (x)-axis. In this interval the signs are (+), (-), (-), so the product is positive. Tip: the product of two negative factors is positive.
Step 3
Exam Tip
इस अंतराल में चिह्न (+), (-), (-) हैं, इसलिए गुणनफल धनात्मक है। टिप: दो ऋणात्मक कारकों का गुणन धनात्मक होता है।
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Question 7/115
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि ग्राफ (x)-अक्ष को ((-10,0)) और ((22,0)) पर काटता है, तो (y)-अक्ष से समान दूरी वाले शून्यक बनाने के लिए कौन सा परिवर्तन चाहिए?
If a graph cuts the (x)-axis at ((-10,0)) and ((22,0)), what change is needed to make the zeroes equally distant from the (y)-axis?
#symmetry
#y axis
#zeroes
A (22) को (10) करना होगा / (22) must be changed to (10)
B (-10) को (0) करना होगा / (-10) must be changed to (0)
C दोनों को ऋणात्मक करना होगा / Both must be made negative
D कोई परिवर्तन नहीं चाहिए / No change is needed
Explanation opens after your attempt
Correct Answer
A. (22) को (10) करना होगा / (22) must be changed to (10)
Step 1
Concept
For equal distance from the (y)-axis, zeroes should be opposites, so (10) is needed with (-10). Tip: symmetric zeroes are (a) and (-a).
Step 2
Why this answer is correct
The correct answer is A. (22) को (10) करना होगा / (22) must be changed to (10). For equal distance from the (y)-axis, zeroes should be opposites, so (10) is needed with (-10). Tip: symmetric zeroes are (a) and (-a).
Step 3
Exam Tip
(y)-अक्ष से समान दूरी के लिए शून्यक विपरीत होने चाहिए, इसलिए (-10) के साथ (10) चाहिए। टिप: सममित शून्यक (a) और (-a) होते हैं।
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Question 8/115
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(x)=x-2 -hx) है, तो ग्राफ के (x)-अक्ष कटान कौन से होंगे?
If (p(x)=x-2 -hx), what will be the (x)-axis intersections of the graph?
#symbolic factorization
#intercepts
#zeroes
A ((0,0)) और ((h,0)) / ((0,0)) and ((h,0))
B ((0,0)) और ((-h,0)) / ((0,0)) and ((-h,0))
C ((h,0)) और ((-h,0)) / ((h,0)) and ((-h,0))
D ((0,h)) और ((h,0)) / ((0,h)) and ((h,0))
Explanation opens after your attempt
Correct Answer
A. ((0,0)) और ((h,0)) / ((0,0)) and ((h,0))
Step 1
Concept
(x-2 -hx=x(x-h)), so the zeroes are (0) and (h). Tip: factor out the common (x).
Step 2
Why this answer is correct
The correct answer is A. ((0,0)) और ((h,0)) / ((0,0)) and ((h,0)). (x-2 -hx=x(x-h)), so the zeroes are (0) and (h). Tip: factor out the common (x).
Step 3
Exam Tip
(x-2 -hx=x(x-h)) है, इसलिए शून्यक (0) और (h) हैं। टिप: सामान्य (x) गुणनखंड निकालें।
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Question 9/115
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि ग्राफ के (x)-अक्ष कटान ((0,0)), ((g,0)), ((-g,0)) हैं, जहाँ \(g\neq0\), तो शून्यकों का योग क्या होगा?
If the (x)-axis intersections of a graph are ((0,0)), ((g,0)), ((-g,0)), where \(g\neq0\), what will be the sum of the zeroes?
#origin
#symbolic sum
#zeroes
A (0)
B \(g^2\)
C \(-g^2\)
D (g)
Explanation opens after your attempt
Step 1
Concept
The zeroes are (0), (g), (-g), so the sum is (0). Tip: opposite numbers cancel each other.
Step 2
Why this answer is correct
The correct answer is A. (0). The zeroes are (0), (g), (-g), so the sum is (0). Tip: opposite numbers cancel each other.
Step 3
Exam Tip
शून्यक (0), (g), (-g) हैं, इसलिए योग (0) होगा। टिप: विपरीत संख्याएँ एक-दूसरे को काट देती हैं।
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Question 10/115
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि ग्राफ (x)-अक्ष को ((10,0)) और ((26,0)) पर काटता है, तो इनके बीच (x=18) की स्थिति क्या है?
If a graph cuts the (x)-axis at ((10,0)) and ((26,0)), what is the position of (x=18) between them?
#midpoint
#zeroes
#graph reasoning
A यह दोनों शून्यकों का मध्य है / It is the midpoint of the two zeroes
B यह शून्यक अवश्य है / It is certainly a zero
C यह (y)-अक्ष कटान है / It is a (y)-axis intercept
D यह सबसे छोटा शून्यक है / It is the smallest zero
Explanation opens after your attempt
Correct Answer
A. यह दोनों शून्यकों का मध्य है / It is the midpoint of the two zeroes
Step 1
Concept
\(18=\frac{10+26}{2}\), so it is the midpoint of the two zeroes. Tip: the midpoint value need not be a zero.
Step 2
Why this answer is correct
The correct answer is A. यह दोनों शून्यकों का मध्य है / It is the midpoint of the two zeroes. \(18=\frac{10+26}{2}\), so it is the midpoint of the two zeroes. Tip: the midpoint value need not be a zero.
Step 3
Exam Tip
\(18=\frac{10+26}{2}\), इसलिए यह दोनों शून्यकों का मध्य है। टिप: मध्य मान का शून्यक होना जरूरी नहीं।
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Question 11/115
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(x)=x-3 -12x-2 +35x) है, तो ग्राफ के शून्यकों का समूह कौन सा है?
If (p(x)=x-3 -12x-2 +35x), what is the set of zeroes of the graph?
#cubic factorization
#zeroes
#graph
A (0,5,7)
B (0,-5,-7)
C (5,7,12)
D केवल (0) / Only (0)
Explanation opens after your attempt
Correct Answer
A. (0,5,7)
Step 1
Concept
(x-3 -12x-2 +35x=x(x-5)(x-7)), so the zeroes are (0), (5), (7). Tip: first take (x) as the common factor.
Step 2
Why this answer is correct
The correct answer is A. (0,5,7). (x-3 -12x-2 +35x=x(x-5)(x-7)), so the zeroes are (0), (5), (7). Tip: first take (x) as the common factor.
Step 3
Exam Tip
(x-3 -12x-2 +35x=x(x-5)(x-7)) है, इसलिए शून्यक (0), (5), (7) हैं। टिप: पहले (x) सामान्य गुणनखंड निकालें।
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Question 12/115
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि ग्राफ के (x)-अक्ष कटान ((s-4 ,0)), ((s+1,0)), ((s+7,0)) हैं, तो शून्यकों का माध्य क्या है?
If the (x)-axis intersections of a graph are ((s-4 ,0)), ((s+1,0)), ((s+7,0)), what is the mean of the zeroes?
#symbolic mean
#zeroes
#coordinates
A \(s+\frac{4}{3}\)
B (3s+4)
C (s-4 )
D (s+7)
Explanation opens after your attempt
Correct Answer
A. \(s+\frac{4}{3}\)
Step 1
Concept
The mean is (\frac{(s-4 )+(s+1)+(s+7)}{3}=s+\frac{4}{3}). Tip: take the average even for symbolic zeroes.
Step 2
Why this answer is correct
The correct answer is A. \(s+\frac{4}{3}\). The mean is (\frac{(s-4 )+(s+1)+(s+7)}{3}=s+\frac{4}{3}). Tip: take the average even for symbolic zeroes.
Step 3
Exam Tip
माध्य (\frac{(s-4 )+(s+1)+(s+7)}{3}=s+\frac{4}{3}) है। टिप: प्रतीकात्मक शून्यकों में भी औसत लें।
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Question 13/115
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि कोई ग्राफ (y)-अक्ष को मूल बिंदु पर काटता है और (x=-9) पर (x)-अक्ष को काटता है, तो शून्यक कौन से हैं?
If a graph cuts the (y)-axis at the origin and cuts the (x)-axis at (x=-9), what are the zeroes?
#origin
#x intercept
#zeroes
A (0) और (-9) / (0) and (-9)
B केवल (-9) / Only (-9)
C केवल (0) / Only (0)
D (0) और (9) / (0) and (9)
Explanation opens after your attempt
Correct Answer
A. (0) और (-9) / (0) and (-9)
Step 1
Concept
The origin is also on the (x)-axis, and (x=-9) is another (x)-axis intersection. Tip: count ((0,0)) as zero (0).
Step 2
Why this answer is correct
The correct answer is A. (0) और (-9) / (0) and (-9). The origin is also on the (x)-axis, and (x=-9) is another (x)-axis intersection. Tip: count ((0,0)) as zero (0).
Step 3
Exam Tip
मूल बिंदु (x)-अक्ष पर भी है और (x=-9) भी (x)-अक्ष कटान है। टिप: ((0,0)) को शून्यक (0) के रूप में गिनें।
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Question 14/115
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
किसी परवलय के (x)-अक्ष कटान ((-17,0)) और ((9,0)) हैं। उसके शून्यकों के मध्यबिंदु का निर्देशांक क्या है?
The (x)-axis intersections of a parabola are ((-17,0)) and ((9,0)). What is the coordinate of the midpoint of its zeroes?
#midpoint
#zeroes
#parabola
A ((-4,0))
B ((-8,0))
C ((4,0))
D ((0,-4))
Explanation opens after your attempt
Correct Answer
A. ((-4,0))
Step 1
Concept
The midpoint is (\left\(\frac{-17+9}{2},0\right\)=(-4,0)). Tip: on the (x)-axis the midpoint has (y=0).
Step 2
Why this answer is correct
The correct answer is A. ((-4,0)). The midpoint is (\left\(\frac{-17+9}{2},0\right\)=(-4,0)). Tip: on the (x)-axis the midpoint has (y=0).
Step 3
Exam Tip
मध्यबिंदु (\left\(\frac{-17+9}{2},0\right\)=(-4,0)) है। टिप: (x)-अक्ष पर मध्यबिंदु का (y)-मान (0) रहता है।
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Question 15/115
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(x)=x-3 -9x-2 +18x) है, तो ग्राफ के शून्यकों का माध्य क्या है?
If (p(x)=x-3 -9x-2 +18x), what is the mean of the zeroes of the graph?
#cubic factorization
#mean
#zeroes
A (3)
B (6)
C (9)
D \(\frac{18}{3}\)
Explanation opens after your attempt
Step 1
Concept
(p(x)=x(x-3)(x-6)), so the zeroes are (0), (3), (6), and the mean is (3). Tip: factor first.
Step 2
Why this answer is correct
The correct answer is A. (3). (p(x)=x(x-3)(x-6)), so the zeroes are (0), (3), (6), and the mean is (3). Tip: factor first.
Step 3
Exam Tip
(p(x)=x(x-3)(x-6)) है इसलिए शून्यक (0), (3), (6) और माध्य (3) है। टिप: पहले गुणनखंड करें।
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Question 16/115
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 17/115
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
किसी परवलय का एक शून्यक (-10) है और दूसरा शून्यक पहले से (18) अधिक है। सममिति अक्ष क्या होगा?
One zero of a parabola is (-10), and the other zero is (18) more than the first. What is the axis of symmetry?
#axis symmetry
#word problem
#zeroes
A (x=-1)
B (x=1)
C (x=8)
D (x=-8)
Explanation opens after your attempt
Step 1
Concept
The other zero is (8), and the average is \(\frac{-10+8}{2}=-1\). Tip: the axis of symmetry is the average of two zeroes.
Step 2
Why this answer is correct
The correct answer is A. (x=-1). The other zero is (8), and the average is \(\frac{-10+8}{2}=-1\). Tip: the axis of symmetry is the average of two zeroes.
Step 3
Exam Tip
दूसरा शून्यक (8) है और औसत \(\frac{-10+8}{2}=-1\) है। टिप: सममिति अक्ष दो शून्यकों का औसत है।
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Question 18/115
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(x)=x-2 -(2n+3)x+n(n+3)) है, तो ग्राफ के (x)-अक्ष कटान कौन से होंगे?
If (p(x)=x-2 -(2n+3)x+n(n+3)), what will be the (x)-axis intersections of the graph?
#symbolic factorization
#intercepts
#zeroes
A ((n,0)) और ((n+3,0)) / ((n,0)) and ((n+3,0))
B ((0,n)) और ((0,n+3)) / ((0,n)) and ((0,n+3))
C ((-n,0)) और ((-n-3,0)) / ((-n,0)) and ((-n-3,0))
D ((n,n+3)) और ((n+3,n)) / ((n,n+3)) and ((n+3,n))
Explanation opens after your attempt
Correct Answer
A. ((n,0)) और ((n+3,0)) / ((n,0)) and ((n+3,0))
Step 1
Concept
The polynomial is ((x-n)(x-(n+3))), so the zeroes are (n) and (n+3). Tip: write zeroes as ((x,0)).
Step 2
Why this answer is correct
The correct answer is A. ((n,0)) और ((n+3,0)) / ((n,0)) and ((n+3,0)). The polynomial is ((x-n)(x-(n+3))), so the zeroes are (n) and (n+3). Tip: write zeroes as ((x,0)).
Step 3
Exam Tip
बहुपद ((x-n)(x-(n+3))) है इसलिए शून्यक (n) और (n+3) हैं। टिप: शून्यकों को ((x,0)) में लिखें।
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Question 19/115
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
एक ऊपर खुलने वाले परवलय के शून्यक (-9) और (3) हैं। (x=-4) पर ग्राफ की स्थिति क्या होगी?
An upward-opening parabola has zeroes (-9) and (3). What will be the position of the graph at (x=-4)?
#sign region
#upward parabola
#zeroes
A (x)-अक्ष के नीचे / Below the (x)-axis
B (x)-अक्ष के ऊपर / Above the (x)-axis
C ठीक (x)-अक्ष पर / On the (x)-axis
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Correct Answer
A. (x)-अक्ष के नीचे / Below the (x)-axis
Step 1
Concept
(x=-4) lies between the two zeroes and an upward-opening parabola stays below there. Tip: check the sign region between zeroes.
Step 2
Why this answer is correct
The correct answer is A. (x)-अक्ष के नीचे / Below the (x)-axis. (x=-4) lies between the two zeroes and an upward-opening parabola stays below there. Tip: check the sign region between zeroes.
Step 3
Exam Tip
(x=-4) दोनों शून्यकों के बीच है और ऊपर खुलने वाला परवलय बीच में नीचे रहता है। टिप: शून्यकों के बीच संकेत क्षेत्र देखें।
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Question 20/115
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि (p(x)=x-2 -2cx+c-2 -25) है, तो ग्राफ के शून्यक कौन से होंगे?
If (p(x)=x-2 -2cx+c-2 -25), what will be the zeroes of the graph?
#symbolic quadratic
#difference of squares
#zeroes
A (c-5) और (c+5) / (c-5) and (c+5)
B (5-c) और (-c-5) / (5-c) and (-c-5)
C (c) और (25) / (c) and (25)
D कोई नहीं / None
Explanation opens after your attempt
Correct Answer
A. (c-5) और (c+5) / (c-5) and (c+5)
Step 1
Concept
It is ((x-c)2 -25), so \(x-c=\pm5\) and the zeroes are (c-5), (c+5). Tip: use difference of squares.
Step 2
Why this answer is correct
The correct answer is A. (c-5) और (c+5) / (c-5) and (c+5). It is ((x-c)2 -25), so \(x-c=\pm5\) and the zeroes are (c-5), (c+5). Tip: use difference of squares.
Step 3
Exam Tip
यह ((x-c)2 -25) है, इसलिए \(x-c=\pm5\) और शून्यक (c-5), (c+5) हैं। टिप: वर्गों के अंतर का उपयोग करें।
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Question 21/115
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि (p(x)=(x-3)(x-6)(x-11)) है, तो (3<x<6) में ग्राफ कहाँ होगा?
If (p(x)=(x-3)(x-6)(x-11)), where will the graph be for (3<x<6)?
#sign analysis
#cubic graph
#zeroes
A (x)-अक्ष के ऊपर / Above the (x)-axis
B (x)-अक्ष के नीचे / Below the (x)-axis
C ठीक (x)-अक्ष पर / On the (x)-axis
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Correct Answer
A. (x)-अक्ष के ऊपर / Above the (x)-axis
Step 1
Concept
In this interval the signs are (+), (-), (-), so the product is positive. Tip: the product of two negative factors is positive.
Step 2
Why this answer is correct
The correct answer is A. (x)-अक्ष के ऊपर / Above the (x)-axis. In this interval the signs are (+), (-), (-), so the product is positive. Tip: the product of two negative factors is positive.
Step 3
Exam Tip
इस अंतराल में चिह्न (+), (-), (-) हैं, इसलिए गुणनफल धनात्मक है। टिप: दो ऋणात्मक कारकों का गुणन धनात्मक होता है।
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Question 22/115
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि ग्राफ (x)-अक्ष को ((-8,0)) और ((18,0)) पर काटता है, तो (y)-अक्ष से समान दूरी वाले शून्यक बनाने के लिए कौन सा परिवर्तन चाहिए?
If a graph cuts the (x)-axis at ((-8,0)) and ((18,0)), what change is needed to make the zeroes equally distant from the (y)-axis?
#symmetry
#y axis
#zeroes
A (18) को (8) करना होगा / (18) must be changed to (8)
B (-8) को (0) करना होगा / (-8) must be changed to (0)
C दोनों को ऋणात्मक करना होगा / Both must be made negative
D कोई परिवर्तन नहीं चाहिए / No change is needed
Explanation opens after your attempt
Correct Answer
A. (18) को (8) करना होगा / (18) must be changed to (8)
Step 1
Concept
For equal distance from the (y)-axis, zeroes should be opposites, so (8) is needed with (-8). Tip: symmetric zeroes are (a) and (-a).
Step 2
Why this answer is correct
The correct answer is A. (18) को (8) करना होगा / (18) must be changed to (8). For equal distance from the (y)-axis, zeroes should be opposites, so (8) is needed with (-8). Tip: symmetric zeroes are (a) and (-a).
Step 3
Exam Tip
(y)-अक्ष से समान दूरी के लिए शून्यक विपरीत होने चाहिए, इसलिए (-8) के साथ (8) चाहिए। टिप: सममित शून्यक (a) और (-a) होते हैं।
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Question 23/115
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि (p(x)=x-2 -ex) है, तो ग्राफ के (x)-अक्ष कटान कौन से होंगे?
If (p(x)=x-2 -ex), what will be the (x)-axis intersections of the graph?
#symbolic factorization
#intercepts
#zeroes
A ((0,0)) और ((e,0)) / ((0,0)) and ((e,0))
B ((0,0)) और ((-e,0)) / ((0,0)) and ((-e,0))
C ((e,0)) और ((-e,0)) / ((e,0)) and ((-e,0))
D ((0,e)) और ((e,0)) / ((0,e)) and ((e,0))
Explanation opens after your attempt
Correct Answer
A. ((0,0)) और ((e,0)) / ((0,0)) and ((e,0))
Step 1
Concept
(x-2 -ex=x(x-e)), so the zeroes are (0) and (e). Tip: factor out the common (x).
Step 2
Why this answer is correct
The correct answer is A. ((0,0)) और ((e,0)) / ((0,0)) and ((e,0)). (x-2 -ex=x(x-e)), so the zeroes are (0) and (e). Tip: factor out the common (x).
Step 3
Exam Tip
(x-2 -ex=x(x-e)) है, इसलिए शून्यक (0) और (e) हैं। टिप: सामान्य (x) गुणनखंड निकालें।
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Question 24/115
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि ग्राफ के (x)-अक्ष कटान ((0,0)), ((d,0)), ((-d,0)) हैं, जहाँ \(d\neq0\), तो शून्यकों का गुणनफल क्या होगा?
If the (x)-axis intersections of a graph are ((0,0)), ((d,0)), ((-d,0)), where \(d\neq0\), what will be the product of the zeroes?
#origin
#symbolic product
#zeroes
A \(d^2\)
B (0)
C \(-d^2\)
D (d)
Explanation opens after your attempt
Step 1
Concept
The zeroes include (0), so the product is (0). Tip: (0) makes any product (0).
Step 2
Why this answer is correct
The correct answer is B. (0). The zeroes include (0), so the product is (0). Tip: (0) makes any product (0).
Step 3
Exam Tip
शून्यकों में (0) शामिल है, इसलिए गुणनफल (0) होगा। टिप: (0) किसी भी गुणनफल को (0) बना देता है।
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Question 25/115
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि ग्राफ (x)-अक्ष को ((8,0)) और ((20,0)) पर काटता है, तो इनके बीच (x=14) की स्थिति क्या है?
If a graph cuts the (x)-axis at ((8,0)) and ((20,0)), what is the position of (x=14) between them?
#midpoint
#zeroes
#graph reasoning
A यह दोनों शून्यकों का मध्य है / It is the midpoint of the two zeroes
B यह शून्यक अवश्य है / It is certainly a zero
C यह (y)-अक्ष कटान है / It is a (y)-axis intercept
D यह सबसे छोटा शून्यक है / It is the smallest zero
Explanation opens after your attempt
Correct Answer
A. यह दोनों शून्यकों का मध्य है / It is the midpoint of the two zeroes
Step 1
Concept
\(14=\frac{8+20}{2}\), so it is the midpoint of the two zeroes. Tip: the midpoint value need not be a zero.
Step 2
Why this answer is correct
The correct answer is A. यह दोनों शून्यकों का मध्य है / It is the midpoint of the two zeroes. \(14=\frac{8+20}{2}\), so it is the midpoint of the two zeroes. Tip: the midpoint value need not be a zero.
Step 3
Exam Tip
\(14=\frac{8+20}{2}\), इसलिए यह दोनों शून्यकों का मध्य है। टिप: मध्य मान का शून्यक होना जरूरी नहीं।
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Question 26/115
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि (p(x)=x-3 -10x-2 +24x) है, तो ग्राफ के शून्यकों का समूह कौन सा है?
If (p(x)=x-3 -10x-2 +24x), what is the set of zeroes of the graph?
#cubic factorization
#zeroes
#graph
A (0,4,6)
B (0,-4,-6)
C (4,6,10)
D केवल (0) / Only (0)
Explanation opens after your attempt
Correct Answer
A. (0,4,6)
Step 1
Concept
(x-3 -10x-2 +24x=x(x-4)(x-6)), so the zeroes are (0), (4), (6). Tip: first take (x) as the common factor.
Step 2
Why this answer is correct
The correct answer is A. (0,4,6). (x-3 -10x-2 +24x=x(x-4)(x-6)), so the zeroes are (0), (4), (6). Tip: first take (x) as the common factor.
Step 3
Exam Tip
(x-3 -10x-2 +24x=x(x-4)(x-6)) है, इसलिए शून्यक (0), (4), (6) हैं। टिप: पहले (x) सामान्य गुणनखंड निकालें।
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Question 27/115
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि ग्राफ के (x)-अक्ष कटान ((r-1,0)), ((r+2,0)), ((r+5,0)) हैं, तो शून्यकों का माध्य क्या है?
If the (x)-axis intersections of a graph are ((r-1,0)), ((r+2,0)), ((r+5,0)), what is the mean of the zeroes?
#symbolic mean
#zeroes
#coordinates
A (r+2)
B (3r+6)
C (r-2)
D (r+5)
Explanation opens after your attempt
Step 1
Concept
The mean is (\frac{(r-1)+(r+2)+(r+5)}{3}=r+2). Tip: take the average even for symbolic zeroes.
Step 2
Why this answer is correct
The correct answer is A. (r+2). The mean is (\frac{(r-1)+(r+2)+(r+5)}{3}=r+2). Tip: take the average even for symbolic zeroes.
Step 3
Exam Tip
माध्य (\frac{(r-1)+(r+2)+(r+5)}{3}=r+2) है। टिप: प्रतीकात्मक शून्यकों में भी औसत लें।
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Question 28/115
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि कोई ग्राफ (y)-अक्ष को मूल बिंदु पर काटता है और (x=6) पर (x)-अक्ष को काटता है, तो शून्यक कौन से हैं?
If a graph cuts the (y)-axis at the origin and cuts the (x)-axis at (x=6), what are the zeroes?
#origin
#x intercept
#zeroes
A (0) और (6) / (0) and (6)
B केवल (6) / Only (6)
C केवल (0) / Only (0)
D (0) और (-6) / (0) and (-6)
Explanation opens after your attempt
Correct Answer
A. (0) और (6) / (0) and (6)
Step 1
Concept
The origin is also on the (x)-axis, and (x=6) is another (x)-axis intersection. Tip: count ((0,0)) as zero (0).
Step 2
Why this answer is correct
The correct answer is A. (0) और (6) / (0) and (6). The origin is also on the (x)-axis, and (x=6) is another (x)-axis intersection. Tip: count ((0,0)) as zero (0).
Step 3
Exam Tip
मूल बिंदु (x)-अक्ष पर भी है और (x=6) भी (x)-अक्ष कटान है। टिप: ((0,0)) को शून्यक (0) के रूप में गिनें।
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Question 29/115
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
किसी परवलय के (x)-अक्ष कटान ((-13,0)) और ((7,0)) हैं। उसके शून्यकों के मध्यबिंदु का निर्देशांक क्या है?
The (x)-axis intersections of a parabola are ((-13,0)) and ((7,0)). What is the coordinate of the midpoint of its zeroes?
#midpoint
#zeroes
#parabola
A ((-3,0))
B ((-10,0))
C ((3,0))
D ((0,-3))
Explanation opens after your attempt
Correct Answer
A. ((-3,0))
Step 1
Concept
The midpoint is (\left\(\frac{-13+7}{2},0\right\)=(-3,0)). Tip: on the (x)-axis the midpoint has (y=0).
Step 2
Why this answer is correct
The correct answer is A. ((-3,0)). The midpoint is (\left\(\frac{-13+7}{2},0\right\)=(-3,0)). Tip: on the (x)-axis the midpoint has (y=0).
Step 3
Exam Tip
मध्यबिंदु (\left\(\frac{-13+7}{2},0\right\)=(-3,0)) है। टिप: (x)-अक्ष पर मध्यबिंदु का (y)-मान (0) रहता है।
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Question 30/115
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि (p(x)=x-3 -7x-2 +10x) है, तो ग्राफ के शून्यकों का माध्य क्या है?
If (p(x)=x-3 -7x-2 +10x), what is the mean of the zeroes of the graph?
#cubic factorization
#mean
#zeroes
A \(\frac{7}{3}\)
B (7)
C (10)
D \(\frac{10}{3}\)
Explanation opens after your attempt
Correct Answer
A. \(\frac{7}{3}\)
Step 1
Concept
(p(x)=x(x-5)(x-2)), so the zeroes are (0), (2), (5), and the mean is \(\frac{7}{3}\). Tip: factor first.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{7}{3}\). (p(x)=x(x-5)(x-2)), so the zeroes are (0), (2), (5), and the mean is \(\frac{7}{3}\). Tip: factor first.
Step 3
Exam Tip
(p(x)=x(x-5)(x-2)) है, इसलिए शून्यक (0), (2), (5) और माध्य \(\frac{7}{3}\) है। टिप: पहले गुणनखंड करें।
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