65 results found for "x-axis-intersections" in Class 10.
Question
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि किसी ग्राफ के (x)-अक्ष कटान ((-4,0)), ((6,0)), ((16,0)) हैं, तो इनके शून्यकों का माध्य क्या है?
If the (x)-axis intersections of a graph are ((-4,0)), ((6,0)), ((16,0)), what is the mean of their zeroes?
#mean of zeroes
#graph
#intercepts
A (6)
B (18)
C (-6)
D (16)
Explanation opens after your attempt
Step 1
Concept
The mean is \(\frac{-4+6+16}{3}=6\). Tip: first read the (x)-values from intersection points.
Step 2
Why this answer is correct
The correct answer is A. (6). The mean is \(\frac{-4+6+16}{3}=6\). Tip: first read the (x)-values from intersection points.
Step 3
Exam Tip
माध्य \(\frac{-4+6+16}{3}=6\) है। टिप: पहले कटान बिंदुओं से (x)-मान पढ़ें।
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Question
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
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
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(x)=x-4 -1296) है, तो वास्तविक (x)-अक्ष कटान कौन से हैं?
If (p(x)=x-4 -1296), what are the real (x)-axis intersections?
#quartic
#real zeroes
#graph
A ((-6,0)) और ((6,0)) / ((-6,0)) and ((6,0))
B ((-36,0)) और ((36,0)) / ((-36,0)) and ((36,0))
C ((0,0)), ((-6,0)), ((6,0))
D कोई नहीं / None
Explanation opens after your attempt
Correct Answer
A. ((-6,0)) और ((6,0)) / ((-6,0)) and ((6,0))
Step 1
Concept
(x-4 -1296=\(x^2-36\)\(x^2+36\)), and the real zeroes are only \(\pm6\). Tip: \(x^2+36\) gives no real zero.
Step 2
Why this answer is correct
The correct answer is A. ((-6,0)) और ((6,0)) / ((-6,0)) and ((6,0)). (x-4 -1296=\(x^2-36\)\(x^2+36\)), and the real zeroes are only \(\pm6\). Tip: \(x^2+36\) gives no real zero.
Step 3
Exam Tip
(x-4 -1296=\(x^2-36\)\(x^2+36\)) है और वास्तविक शून्यक केवल \(\pm6\) हैं। टिप: \(x^2+36\) वास्तविक शून्यक नहीं देता।
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Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(x)=36x-2 -49) है, तो ग्राफ के (x)-अक्ष कटान कौन से हैं?
If (p(x)=36x-2 -49), what are the (x)-axis intersections of the graph?
#difference of squares
#fraction zeroes
#graph
A (\left\(\frac{7}{6},0\right\)) और (\left\(-\frac{7}{6},0\right\)) / (\left\(\frac{7}{6},0\right\)) and (\left\(-\frac{7}{6},0\right\))
B ((7,0)) और ((-7,0)) / ((7,0)) and ((-7,0))
C (\left\(\frac{6}{7},0\right\)) और (\left\(-\frac{6}{7},0\right\)) / (\left\(\frac{6}{7},0\right\)) and (\left\(-\frac{6}{7},0\right\))
D कोई नहीं / None
Explanation opens after your attempt
Correct Answer
A. (\left\(\frac{7}{6},0\right\)) और (\left\(-\frac{7}{6},0\right\)) / (\left\(\frac{7}{6},0\right\)) and (\left\(-\frac{7}{6},0\right\))
Step 1
Concept
From \(36x^2-49=0\), \(x=\pm\frac{7}{6}\). Tip: treat \(36x^2\) as ((6x)2 ).
Step 2
Why this answer is correct
The correct answer is A. (\left\(\frac{7}{6},0\right\)) और (\left\(-\frac{7}{6},0\right\)) / (\left\(\frac{7}{6},0\right\)) and (\left\(-\frac{7}{6},0\right\)). From \(36x^2-49=0\), \(x=\pm\frac{7}{6}\). Tip: treat \(36x^2\) as ((6x)2 ).
Step 3
Exam Tip
\(36x^2-49=0\) से \(x=\pm\frac{7}{6}\) मिलता है। टिप: \(36x^2\) को ((6x)2 ) समझें।
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Question
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(x)=x-2 -13x+k) का एक शून्यक (6) है, तो दूसरा शून्यक और (x)-अक्ष कटान क्या होंगे?
If (p(x)=x-2 -13x+k) has one zero (6), what will be the other zero and the (x)-axis intersections?
#missing zero
#quadratic
#intercepts
A दूसरा (7), कटान ((6,0)), ((7,0)) / Other (7), intersections ((6,0)), ((7,0))
B दूसरा (-7), कटान ((6,0)), ((-7,0)) / Other (-7), intersections ((6,0)), ((-7,0))
C दूसरा (13), कटान ((6,0)), ((13,0)) / Other (13), intersections ((6,0)), ((13,0))
D दूसरा (0), कटान ((6,0)), ((0,0)) / Other (0), intersections ((6,0)), ((0,0))
Explanation opens after your attempt
Correct Answer
A. दूसरा (7), कटान ((6,0)), ((7,0)) / Other (7), intersections ((6,0)), ((7,0))
Step 1
Concept
In the quadratic, the sum of zeroes is (13), so the other zero is (7). Tip: convert a zero into ((x,0)).
Step 2
Why this answer is correct
The correct answer is A. दूसरा (7), कटान ((6,0)), ((7,0)) / Other (7), intersections ((6,0)), ((7,0)). In the quadratic, the sum of zeroes is (13), so the other zero is (7). Tip: convert a zero into ((x,0)).
Step 3
Exam Tip
द्विघात में शून्यकों का योग (13) है, इसलिए दूसरा शून्यक (7) है। टिप: शून्यक को ((x,0)) में बदलें।
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Question
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
Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(x)=x-2 -13x-68) है, तो ग्राफ के (x)-अक्ष कटान कौन से हैं?
If (p(x)=x-2 -13x-68), what are the (x)-axis intersections of the graph?
#quadratic factorization
#intercepts
#graph
A ((17,0)) और ((-4,0)) / ((17,0)) and ((-4,0))
B ((-17,0)) और ((4,0)) / ((-17,0)) and ((4,0))
C ((0,17)) और ((0,-4)) / ((0,17)) and ((0,-4))
D ((68,0)) और ((-13,0)) / ((68,0)) and ((-13,0))
Explanation opens after your attempt
Correct Answer
A. ((17,0)) और ((-4,0)) / ((17,0)) and ((-4,0))
Step 1
Concept
(x-2 -13x-68=(x-17)(x+4)), so the zeroes are (17) and (-4). Tip: write intersection points from factors.
Step 2
Why this answer is correct
The correct answer is A. ((17,0)) और ((-4,0)) / ((17,0)) and ((-4,0)). (x-2 -13x-68=(x-17)(x+4)), so the zeroes are (17) and (-4). Tip: write intersection points from factors.
Step 3
Exam Tip
(x-2 -13x-68=(x-17)(x+4)) है, इसलिए शून्यक (17) और (-4) हैं। टिप: गुणनखंडों से कटान बिंदु लिखें।
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Question
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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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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Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि किसी ग्राफ के (x)-अक्ष कटान ((-3,0)), ((5,0)), ((13,0)) हैं, तो इनके शून्यकों का माध्य क्या है?
If the (x)-axis intersections of a graph are ((-3,0)), ((5,0)), ((13,0)), what is the mean of their zeroes?
#mean of zeroes
#graph
#intercepts
A (5)
B (15)
C (-5)
D (13)
Explanation opens after your attempt
Step 1
Concept
The mean is \(\frac{-3+5+13}{3}=5\). Tip: first read the (x)-values from intersection points.
Step 2
Why this answer is correct
The correct answer is A. (5). The mean is \(\frac{-3+5+13}{3}=5\). Tip: first read the (x)-values from intersection points.
Step 3
Exam Tip
माध्य \(\frac{-3+5+13}{3}=5\) है। टिप: पहले कटान बिंदुओं से (x)-मान पढ़ें।
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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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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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Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि (p(x)=x-4 -625) है, तो वास्तविक (x)-अक्ष कटान कौन से हैं?
If (p(x)=x-4 -625), what are the real (x)-axis intersections?
#quartic
#real zeroes
#graph
A ((-5,0)) और ((5,0)) / ((-5,0)) and ((5,0))
B ((-25,0)) और ((25,0)) / ((-25,0)) and ((25,0))
C ((0,0)), ((-5,0)), ((5,0))
D कोई नहीं / None
Explanation opens after your attempt
Correct Answer
A. ((-5,0)) और ((5,0)) / ((-5,0)) and ((5,0))
Step 1
Concept
(x-4 -625=\(x^2-25\)\(x^2+25\)), and the real zeroes are only \(\pm5\). Tip: \(x^2+25\) gives no real zero.
Step 2
Why this answer is correct
The correct answer is A. ((-5,0)) और ((5,0)) / ((-5,0)) and ((5,0)). (x-4 -625=\(x^2-25\)\(x^2+25\)), and the real zeroes are only \(\pm5\). Tip: \(x^2+25\) gives no real zero.
Step 3
Exam Tip
(x-4 -625=\(x^2-25\)\(x^2+25\)) है और वास्तविक शून्यक केवल \(\pm5\) हैं। टिप: \(x^2+25\) वास्तविक शून्यक नहीं देता।
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Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि (p(x)=25x-2 -36) है, तो ग्राफ के (x)-अक्ष कटान कौन से हैं?
If (p(x)=25x-2 -36), what are the (x)-axis intersections of the graph?
#difference of squares
#fraction zeroes
#graph
A (\left\(\frac{6}{5},0\right\)) और (\left\(-\frac{6}{5},0\right\)) / (\left\(\frac{6}{5},0\right\)) and (\left\(-\frac{6}{5},0\right\))
B ((6,0)) और ((-6,0)) / ((6,0)) and ((-6,0))
C (\left\(\frac{5}{6},0\right\)) और (\left\(-\frac{5}{6},0\right\)) / (\left\(\frac{5}{6},0\right\)) and (\left\(-\frac{5}{6},0\right\))
D कोई नहीं / None
Explanation opens after your attempt
Correct Answer
A. (\left\(\frac{6}{5},0\right\)) और (\left\(-\frac{6}{5},0\right\)) / (\left\(\frac{6}{5},0\right\)) and (\left\(-\frac{6}{5},0\right\))
Step 1
Concept
From \(25x^2-36=0\), \(x=\pm\frac{6}{5}\). Tip: treat \(25x^2\) as ((5x)2 ).
Step 2
Why this answer is correct
The correct answer is A. (\left\(\frac{6}{5},0\right\)) और (\left\(-\frac{6}{5},0\right\)) / (\left\(\frac{6}{5},0\right\)) and (\left\(-\frac{6}{5},0\right\)). From \(25x^2-36=0\), \(x=\pm\frac{6}{5}\). Tip: treat \(25x^2\) as ((5x)2 ).
Step 3
Exam Tip
\(25x^2-36=0\) से \(x=\pm\frac{6}{5}\) मिलता है। टिप: \(25x^2\) को ((5x)2 ) समझें।
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Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि (p(x)=x-2 -11x+k) का एक शून्यक (4) है, तो दूसरा शून्यक और (x)-अक्ष कटान क्या होंगे?
If (p(x)=x-2 -11x+k) has one zero (4), what will be the other zero and the (x)-axis intersections?
#missing zero
#quadratic
#intercepts
A दूसरा (7), कटान ((4,0)), ((7,0)) / Other (7), intersections ((4,0)), ((7,0))
B दूसरा (-7), कटान ((4,0)), ((-7,0)) / Other (-7), intersections ((4,0)), ((-7,0))
C दूसरा (11), कटान ((4,0)), ((11,0)) / Other (11), intersections ((4,0)), ((11,0))
D दूसरा (0), कटान ((4,0)), ((0,0)) / Other (0), intersections ((4,0)), ((0,0))
Explanation opens after your attempt
Correct Answer
A. दूसरा (7), कटान ((4,0)), ((7,0)) / Other (7), intersections ((4,0)), ((7,0))
Step 1
Concept
In the quadratic, the sum of zeroes is (11), so the other zero is (7). Tip: convert a zero into ((x,0)).
Step 2
Why this answer is correct
The correct answer is A. दूसरा (7), कटान ((4,0)), ((7,0)) / Other (7), intersections ((4,0)), ((7,0)). In the quadratic, the sum of zeroes is (11), so the other zero is (7). Tip: convert a zero into ((x,0)).
Step 3
Exam Tip
द्विघात में शून्यकों का योग (11) है, इसलिए दूसरा शून्यक (7) है। टिप: शून्यक को ((x,0)) में बदलें।
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Question
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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Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि (p(x)=x-2 -9x-52) है, तो ग्राफ के (x)-अक्ष कटान कौन से हैं?
If (p(x)=x-2 -9x-52), what are the (x)-axis intersections of the graph?
#quadratic factorization
#intercepts
#graph
A ((13,0)) और ((-4,0)) / ((13,0)) and ((-4,0))
B ((-13,0)) और ((4,0)) / ((-13,0)) and ((4,0))
C ((0,13)) और ((0,-4)) / ((0,13)) and ((0,-4))
D ((52,0)) और ((-9,0)) / ((52,0)) and ((-9,0))
Explanation opens after your attempt
Correct Answer
A. ((13,0)) और ((-4,0)) / ((13,0)) and ((-4,0))
Step 1
Concept
(x-2 -9x-52=(x-13)(x+4)), so the zeroes are (13) and (-4). Tip: write intersection points from factors.
Step 2
Why this answer is correct
The correct answer is A. ((13,0)) और ((-4,0)) / ((13,0)) and ((-4,0)). (x-2 -9x-52=(x-13)(x+4)), so the zeroes are (13) and (-4). Tip: write intersection points from factors.
Step 3
Exam Tip
(x-2 -9x-52=(x-13)(x+4)) है, इसलिए शून्यक (13) और (-4) हैं। टिप: गुणनखंडों से कटान बिंदु लिखें।
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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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Expert Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि (p(x)=x-2 -(2m-1)x+m(m-1 )) है, तो ग्राफ के (x)-अक्ष कटान कौन से होंगे?
If (p(x)=x-2 -(2m-1)x+m(m-1 )), what will be the (x)-axis intersections of the graph?
#symbolic factorization
#intercepts
#zeroes
A ((m,0)) और ((m-1 ,0)) / ((m,0)) and ((m-1 ,0))
B ((0,m)) और ((0,m-1 )) / ((0,m)) and ((0,m-1 ))
C ((-m,0)) और ((1-m,0)) / ((-m,0)) and ((1-m,0))
D ((m,m-1 )) और ((m-1 ,m)) / ((m,m-1 )) and ((m-1 ,m))
Explanation opens after your attempt
Correct Answer
A. ((m,0)) और ((m-1 ,0)) / ((m,0)) and ((m-1 ,0))
Step 1
Concept
The polynomial is ((x-m)(x-(m-1 ))), so the zeroes are (m) and (m-1 ). Tip: write zeroes as ((x,0)).
Step 2
Why this answer is correct
The correct answer is A. ((m,0)) और ((m-1 ,0)) / ((m,0)) and ((m-1 ,0)). The polynomial is ((x-m)(x-(m-1 ))), so the zeroes are (m) and (m-1 ). Tip: write zeroes as ((x,0)).
Step 3
Exam Tip
बहुपद ((x-m)(x-(m-1 ))) है, इसलिए शून्यक (m) और (m-1 ) हैं। टिप: शून्यकों को ((x,0)) में लिखें।
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Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि किसी ग्राफ के (x)-अक्ष कटान ((-2,0)), ((4,0)), ((10,0)) हैं तो इनके शून्यकों का माध्य क्या है?
If the (x)-axis intersections of a graph are ((-2,0)), ((4,0)), ((10,0)), what is the mean of their zeroes?
#mean of zeroes
#graph
#intercepts
A (4)
B (12)
C (-4)
D (10)
Explanation opens after your attempt
Step 1
Concept
The mean is \(\frac{-2+4+10}{3}=4\). Tip: first read the (x)-values from intersection points.
Step 2
Why this answer is correct
The correct answer is A. (4). The mean is \(\frac{-2+4+10}{3}=4\). Tip: first read the (x)-values from intersection points.
Step 3
Exam Tip
माध्य \(\frac{-2+4+10}{3}=4\) है। टिप: पहले कटान बिंदुओं से (x)-मान पढ़ें।
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Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि (p(x)=x-2 -cx) है तो ग्राफ के (x)-अक्ष कटान कौन से होंगे?
If (p(x)=x-2 -cx), what will be the (x)-axis intersections of the graph?
#symbolic factorization
#intercepts
#zeroes
A ((0,0)) और ((c,0)) / ((0,0)) and ((c,0))
B ((0,0)) और ((-c,0)) / ((0,0)) and ((-c,0))
C ((c,0)) और ((-c,0)) / ((c,0)) and ((-c,0))
D ((0,c)) और ((c,0)) / ((0,c)) and ((c,0))
Explanation opens after your attempt
Correct Answer
A. ((0,0)) और ((c,0)) / ((0,0)) and ((c,0))
Step 1
Concept
(x-2 -cx=x(x-c)), so the zeroes are (0) and (c). Tip: factor out the common (x).
Step 2
Why this answer is correct
The correct answer is A. ((0,0)) और ((c,0)) / ((0,0)) and ((c,0)). (x-2 -cx=x(x-c)), so the zeroes are (0) and (c). Tip: factor out the common (x).
Step 3
Exam Tip
(x-2 -cx=x(x-c)) है इसलिए शून्यक (0) और (c) हैं। टिप: सामान्य (x) गुणनखंड निकालें।
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Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि ग्राफ के (x)-अक्ष कटान ((0,0)) और ((d,0)) हैं जहाँ \(d\neq0\), तो शून्यकों का गुणनफल क्या होगा?
If the (x)-axis intersections of a graph are ((0,0)) and ((d,0)), where \(d\neq0\), what will be the product of the zeroes?
#origin
#symbolic product
#zeroes
A (d)
B (0)
C \(d^2\)
D (-d)
Explanation opens after your attempt
Step 1
Concept
The zeroes are (0) and (d), so the product is (0). Tip: if (0) is included, the product is (0).
Step 2
Why this answer is correct
The correct answer is B. (0). The zeroes are (0) and (d), so the product is (0). Tip: if (0) is included, the product is (0).
Step 3
Exam Tip
शून्यक (0) और (d) हैं इसलिए गुणनफल (0) है। टिप: (0) शामिल हो तो गुणनफल (0) होगा।
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Question
Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि (p(x)=x-4 -81) है तो वास्तविक (x)-अक्ष कटान कौन से हैं?
If (p(x)=x-4 -81), what are the real (x)-axis intersections?
#quartic
#real zeroes
#graph
A ((-3,0)) और ((3,0)) / ((-3,0)) and ((3,0))
B ((-9,0)) और ((9,0)) / ((-9,0)) and ((9,0))
C ((0,0)), ((3,0)), ((-3,0))
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
(x-4 -81=\(x^2-9\)\(x^2+9\)), and the real zeroes are only \(\pm3\). Tip: \(x^2+9\) gives no real zero.
Step 2
Why this answer is correct
The correct answer is A. ((-3,0)) और ((3,0)) / ((-3,0)) and ((3,0)). (x-4 -81=\(x^2-9\)\(x^2+9\)), and the real zeroes are only \(\pm3\). Tip: \(x^2+9\) gives no real zero.
Step 3
Exam Tip
(x-4 -81=\(x^2-9\)\(x^2+9\)) है और वास्तविक शून्यक केवल \(\pm3\) हैं। टिप: \(x^2+9\) वास्तविक शून्यक नहीं देता।
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Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि (p(x)=16x-2 -9) है तो ग्राफ के (x)-अक्ष कटान कौन से हैं?
If (p(x)=16x-2 -9), what are the (x)-axis intersections of the graph?
#difference of squares
#fraction zeroes
#graph
A (\left\(\frac{3}{4},0\right\)) और (\left\(-\frac{3}{4},0\right\)) / (\left\(\frac{3}{4},0\right\)) and (\left\(-\frac{3}{4},0\right\))
B ((3,0)) और ((-3,0)) / ((3,0)) and ((-3,0))
C (\left\(\frac{4}{3},0\right\)) और (\left\(-\frac{4}{3},0\right\)) / (\left\(\frac{4}{3},0\right\)) and (\left\(-\frac{4}{3},0\right\))
D कोई नहीं / None
Explanation opens after your attempt
Correct Answer
A. (\left\(\frac{3}{4},0\right\)) और (\left\(-\frac{3}{4},0\right\)) / (\left\(\frac{3}{4},0\right\)) and (\left\(-\frac{3}{4},0\right\))
Step 1
Concept
From \(16x^2-9=0\), \(x=\pm\frac{3}{4}\). Tip: treat \(16x^2\) as ((4x)2 ).
Step 2
Why this answer is correct
The correct answer is A. (\left\(\frac{3}{4},0\right\)) और (\left\(-\frac{3}{4},0\right\)) / (\left\(\frac{3}{4},0\right\)) and (\left\(-\frac{3}{4},0\right\)). From \(16x^2-9=0\), \(x=\pm\frac{3}{4}\). Tip: treat \(16x^2\) as ((4x)2 ).
Step 3
Exam Tip
\(16x^2-9=0\) से \(x=\pm\frac{3}{4}\) मिलता है। टिप: \(16x^2\) को ((4x)2 ) समझें।
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Question
Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि ग्राफ के (x)-अक्ष कटान ((m,0)), ((n,0)), ((r,0)) हैं तो शून्यकों का माध्य क्या होगा?
If the (x)-axis intersections of a graph are ((m,0)), ((n,0)), ((r,0)), what will be the mean of the zeroes?
#symbolic zeroes
#mean
#coordinates
A (m+n+r)
B \(\frac{m+n+r}{3}\)
C (mnr)
D (0)
Explanation opens after your attempt
Correct Answer
B. \(\frac{m+n+r}{3}\)
Step 1
Concept
The zeroes are (m), (n), (r), so the mean is \(\frac{m+n+r}{3}\). Tip: take the first coordinate even in symbolic points.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{m+n+r}{3}\). The zeroes are (m), (n), (r), so the mean is \(\frac{m+n+r}{3}\). Tip: take the first coordinate even in symbolic points.
Step 3
Exam Tip
शून्यक (m), (n), (r) हैं इसलिए माध्य \(\frac{m+n+r}{3}\) है। टिप: प्रतीकात्मक बिंदुओं में भी पहला निर्देशांक लें।
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Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि (p(x)=x-2 -8x-33) है तो ग्राफ के (x)-अक्ष कटान कौन से हैं?
If (p(x)=x-2 -8x-33), what are the (x)-axis intersections of the graph?
#quadratic factorization
#intercepts
#graph
A ((11,0)) और ((-3,0)) / ((11,0)) and ((-3,0))
B ((-11,0)) और ((3,0)) / ((-11,0)) and ((3,0))
C ((0,11)) और ((0,-3)) / ((0,11)) and ((0,-3))
D ((33,0)) और ((-8,0)) / ((33,0)) and ((-8,0))
Explanation opens after your attempt
Correct Answer
A. ((11,0)) और ((-3,0)) / ((11,0)) and ((-3,0))
Step 1
Concept
(x-2 -8x-33=(x-11)(x+3)), so the zeroes are (11) and (-3). Tip: form ((x,0)) points from factors.
Step 2
Why this answer is correct
The correct answer is A. ((11,0)) और ((-3,0)) / ((11,0)) and ((-3,0)). (x-2 -8x-33=(x-11)(x+3)), so the zeroes are (11) and (-3). Tip: form ((x,0)) points from factors.
Step 3
Exam Tip
(x-2 -8x-33=(x-11)(x+3)) है इसलिए शून्यक (11) और (-3) हैं। टिप: गुणनखंडों से बिंदु ((x,0)) बनाएं।
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Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि परवलय के (x)-अक्ष कटान ((-11,0)) और ((5,0)) हैं तो मध्यबिंदु का निर्देशांक क्या है?
If the (x)-axis intersections of a parabola are ((-11,0)) and ((5,0)), what is the coordinate of the midpoint?
#midpoint
#zeroes
#parabola
A ((-3,0))
B ((-6,0))
C ((3,0))
D ((0,-3))
Explanation opens after your attempt
Correct Answer
A. ((-3,0))
Step 1
Concept
The midpoint is (\left\(\frac{-11+5}{2},0\right\)=(-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\(\frac{-11+5}{2},0\right\)=(-3,0)). Tip: on the (x)-axis the midpoint has (y=0).
Step 3
Exam Tip
मध्यबिंदु (\left\(\frac{-11+5}{2},0\right\)=(-3,0)) है। टिप: (x)-अक्ष पर मध्यबिंदु का (y)-मान (0) रहता है।
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Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि (p(x)=x-2 -(u+v)x+uv) है तो ग्राफ के (x)-अक्ष कटान कौन से होंगे?
If (p(x)=x-2 -(u+v)x+uv), what will be the (x)-axis intersections of the graph?
#symbolic factorization
#intercepts
#zeroes
A ((u,0)) और ((v,0)) / ((u,0)) and ((v,0))
B ((0,u)) और ((0,v)) / ((0,u)) and ((0,v))
C ((-u,0)) और ((-v,0)) / ((-u,0)) and ((-v,0))
D ((u,v)) और ((v,u)) / ((u,v)) and ((v,u))
Explanation opens after your attempt
Correct Answer
A. ((u,0)) और ((v,0)) / ((u,0)) and ((v,0))
Step 1
Concept
It is ((x-u)(x-v)), so the zeroes are (u) and (v). Tip: write each zero as the point ((x,0)).
Step 2
Why this answer is correct
The correct answer is A. ((u,0)) और ((v,0)) / ((u,0)) and ((v,0)). It is ((x-u)(x-v)), so the zeroes are (u) and (v). Tip: write each zero as the point ((x,0)).
Step 3
Exam Tip
यह ((x-u)(x-v)) है इसलिए शून्यक (u) और (v) हैं। टिप: शून्यक को ((x,0)) बिंदु के रूप में लिखें।
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Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि किसी ग्राफ के (x)-अक्ष कटान ((-1,0)), ((3,0)), ((7,0)) हैं, तो इनके शून्यकों का माध्य क्या है?
If the (x)-axis intersections of a graph are ((-1,0)), ((3,0)), ((7,0)), what is the mean of their zeroes?
#mean of zeroes
#graph
#intercepts
A (3)
B (9)
C (-3)
D (7)
Explanation opens after your attempt
Step 1
Concept
The mean is \(\frac{-1+3+7}{3}=3\). Tip: first read the (x)-values from intersection points.
Step 2
Why this answer is correct
The correct answer is A. (3). The mean is \(\frac{-1+3+7}{3}=3\). Tip: first read the (x)-values from intersection points.
Step 3
Exam Tip
माध्य \(\frac{-1+3+7}{3}=3\) है। टिप: पहले कटान बिंदुओं से (x)-मान पढ़ें।
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Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(x)=x-2 -bx) है, तो ग्राफ के (x)-अक्ष कटान कौन से होंगे?
If (p(x)=x-2 -bx), what will be the (x)-axis intersections of the graph?
#symbolic factorization
#intercepts
#zeroes
A ((0,0)) और ((b,0)) / ((0,0)) and ((b,0))
B ((0,0)) और ((-b,0)) / ((0,0)) and ((-b,0))
C ((b,0)) और ((-b,0)) / ((b,0)) and ((-b,0))
D ((0,b)) और ((b,0)) / ((0,b)) and ((b,0))
Explanation opens after your attempt
Correct Answer
A. ((0,0)) और ((b,0)) / ((0,0)) and ((b,0))
Step 1
Concept
(x-2 -bx=x(x-b)), so the zeroes are (0) and (b). Tip: factor out the common (x).
Step 2
Why this answer is correct
The correct answer is A. ((0,0)) और ((b,0)) / ((0,0)) and ((b,0)). (x-2 -bx=x(x-b)), so the zeroes are (0) and (b). Tip: factor out the common (x).
Step 3
Exam Tip
(x-2 -bx=x(x-b)) है, इसलिए शून्यक (0) और (b) हैं। टिप: सामान्य (x) गुणनखंड निकालें।
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Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि ग्राफ के (x)-अक्ष कटान ((0,0)) और ((b,0)) हैं, जहाँ \(b\neq0\), तो शून्यकों का योग क्या होगा?
If the (x)-axis intersections of a graph are ((0,0)) and ((b,0)), where \(b\neq0\), what will be the sum of the zeroes?
#origin
#symbolic sum
#zeroes
A (0)
B (b)
C \(b^2\)
D (-b)
Explanation opens after your attempt
Step 1
Concept
The zeroes are (0) and (b), so the sum is (b). Tip: do not forget to include the zero (0) from the origin.
Step 2
Why this answer is correct
The correct answer is B. (b). The zeroes are (0) and (b), so the sum is (b). Tip: do not forget to include the zero (0) from the origin.
Step 3
Exam Tip
शून्यक (0) और (b) हैं, इसलिए योग (b) है। टिप: मूल बिंदु का शून्यक (0) जोड़ना न भूलें।
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Question
Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(x)=x-4 -16) है, तो वास्तविक (x)-अक्ष कटान कौन से हैं?
If (p(x)=x-4 -16), what are the real (x)-axis intersections?
#quartic
#real zeroes
#graph
A ((-2,0)) और ((2,0)) / ((-2,0)) and ((2,0))
B ((-4,0)) और ((4,0)) / ((-4,0)) and ((4,0))
C ((0,0)), ((2,0)), ((-2,0))
D कोई नहीं / None
Explanation opens after your attempt
Correct Answer
A. ((-2,0)) और ((2,0)) / ((-2,0)) and ((2,0))
Step 1
Concept
(x-4 -16=\(x^2-4\)\(x^2+4\)), and the real zeroes are only \(\pm2\). Tip: \(x^2+4\) gives no real zero.
Step 2
Why this answer is correct
The correct answer is A. ((-2,0)) और ((2,0)) / ((-2,0)) and ((2,0)). (x-4 -16=\(x^2-4\)\(x^2+4\)), and the real zeroes are only \(\pm2\). Tip: \(x^2+4\) gives no real zero.
Step 3
Exam Tip
(x-4 -16=\(x^2-4\)\(x^2+4\)) है और वास्तविक शून्यक केवल \(\pm2\) हैं। टिप: \(x^2+4\) वास्तविक शून्यक नहीं देता।
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Question
Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(x)=9x-2 -16) है, तो ग्राफ के (x)-अक्ष कटान कौन से हैं?
If (p(x)=9x-2 -16), what are the (x)-axis intersections of the graph?
#difference of squares
#fraction zeroes
#graph
A (\left\(\frac{4}{3},0\right\)) और (\left\(-\frac{4}{3},0\right\)) / (\left\(\frac{4}{3},0\right\)) and (\left\(-\frac{4}{3},0\right\))
B ((4,0)) और ((-4,0)) / ((4,0)) and ((-4,0))
C (\left\(\frac{3}{4},0\right\)) और (\left\(-\frac{3}{4},0\right\)) / (\left\(\frac{3}{4},0\right\)) and (\left\(-\frac{3}{4},0\right\))
D कोई नहीं / None
Explanation opens after your attempt
Correct Answer
A. (\left\(\frac{4}{3},0\right\)) और (\left\(-\frac{4}{3},0\right\)) / (\left\(\frac{4}{3},0\right\)) and (\left\(-\frac{4}{3},0\right\))
Step 1
Concept
From \(9x^2-16=0\), \(x=\pm\frac{4}{3}\). Tip: treat \(9x^2\) as ((3x)2 ).
Step 2
Why this answer is correct
The correct answer is A. (\left\(\frac{4}{3},0\right\)) और (\left\(-\frac{4}{3},0\right\)) / (\left\(\frac{4}{3},0\right\)) and (\left\(-\frac{4}{3},0\right\)). From \(9x^2-16=0\), \(x=\pm\frac{4}{3}\). Tip: treat \(9x^2\) as ((3x)2 ).
Step 3
Exam Tip
\(9x^2-16=0\) से \(x=\pm\frac{4}{3}\) मिलता है। टिप: \(9x^2\) को ((3x)2 ) समझें।
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Question
Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि ग्राफ के (x)-अक्ष कटान ((a,0)), ((b,0)), ((c,0)) हैं, तो शून्यकों का गुणनफल क्या होगा?
If the (x)-axis intersections of a graph are ((a,0)), ((b,0)), ((c,0)), what will be the product of the zeroes?
#symbolic zeroes
#product
#coordinates
A (a+b+c)
B (abc)
C (0)
D (ab+c)
Explanation opens after your attempt
Step 1
Concept
The zeroes are (a), (b), (c), so their product is (abc). Tip: even in symbolic points, the first coordinate is the zero.
Step 2
Why this answer is correct
The correct answer is B. (abc). The zeroes are (a), (b), (c), so their product is (abc). Tip: even in symbolic points, the first coordinate is the zero.
Step 3
Exam Tip
शून्यक (a), (b), (c) हैं, इसलिए गुणनफल (abc) है। टिप: प्रतीकात्मक बिंदु में भी पहला निर्देशांक शून्यक है।
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Question
Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(x)=x-2 -4x-21) है, तो ग्राफ के (x)-अक्ष कटान कौन से हैं?
If (p(x)=x-2 -4x-21), what are the (x)-axis intersections of the graph?
#quadratic factorization
#intercepts
#graph
A ((7,0)) और ((-3,0)) / ((7,0)) and ((-3,0))
B ((-7,0)) और ((3,0)) / ((-7,0)) and ((3,0))
C ((0,7)) और ((0,-3)) / ((0,7)) and ((0,-3))
D ((21,0)) और ((-4,0)) / ((21,0)) and ((-4,0))
Explanation opens after your attempt
Correct Answer
A. ((7,0)) और ((-3,0)) / ((7,0)) and ((-3,0))
Step 1
Concept
(x-2 -4x-21=(x-7)(x+3)), so the zeroes are (7) and (-3). Tip: form ((x,0)) points from factors.
Step 2
Why this answer is correct
The correct answer is A. ((7,0)) और ((-3,0)) / ((7,0)) and ((-3,0)). (x-2 -4x-21=(x-7)(x+3)), so the zeroes are (7) and (-3). Tip: form ((x,0)) points from factors.
Step 3
Exam Tip
(x-2 -4x-21=(x-7)(x+3)) है, इसलिए शून्यक (7) और (-3) हैं। टिप: गुणनखंडों से बिंदु ((x,0)) बनाएं।
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Question
Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि परवलय के (x)-अक्ष कटान ((-9,0)) और ((3,0)) हैं, तो मध्यबिंदु का निर्देशांक क्या है?
If the (x)-axis intersections of a parabola are ((-9,0)) and ((3,0)), what is the coordinate of the midpoint?
#midpoint
#zeroes
#parabola
A ((-3,0))
B ((-6,0))
C ((3,0))
D ((0,-3))
Explanation opens after your attempt
Correct Answer
A. ((-3,0))
Step 1
Concept
The midpoint is (\left\(\frac{-9+3}{2},0\right\)=(-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\(\frac{-9+3}{2},0\right\)=(-3,0)). Tip: on the (x)-axis the midpoint has (y=0).
Step 3
Exam Tip
मध्यबिंदु (\left\(\frac{-9+3}{2},0\right\)=(-3,0)) है। टिप: (x)-अक्ष पर मध्यबिंदु का (y)-मान (0) रहता है।
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Question
Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(x)=x-2 -(m+n)x+mn) है, तो ग्राफ के (x)-अक्ष कटान कौन से होंगे?
If (p(x)=x-2 -(m+n)x+mn), what will be the (x)-axis intersections of the graph?
#symbolic factorization
#intercepts
#zeroes
A ((m,0)) और ((n,0)) / ((m,0)) and ((n,0))
B ((0,m)) और ((0,n)) / ((0,m)) and ((0,n))
C ((-m,0)) और ((-n,0)) / ((-m,0)) and ((-n,0))
D ((m,n)) और ((n,m)) / ((m,n)) and ((n,m))
Explanation opens after your attempt
Correct Answer
A. ((m,0)) और ((n,0)) / ((m,0)) and ((n,0))
Step 1
Concept
It is ((x-m)(x-n)), so the zeroes are (m) and (n). Tip: write each zero as ((x,0)).
Step 2
Why this answer is correct
The correct answer is A. ((m,0)) और ((n,0)) / ((m,0)) and ((n,0)). It is ((x-m)(x-n)), so the zeroes are (m) and (n). Tip: write each zero as ((x,0)).
Step 3
Exam Tip
यह ((x-m)(x-n)) है इसलिए शून्यक (m) और (n) हैं। टिप: शून्यक को ((x,0)) में लिखें।
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Question
Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि (p(x)=x-2 -ax) है, तो ग्राफ के (x)-अक्ष कटान कौन से होंगे?
If (p(x)=x-2 -ax), what will be the (x)-axis intersections of the graph?
#symbolic factorization
#intercepts
#zeroes
A ((0,0)) और ((a,0)) / ((0,0)) and ((a,0))
B ((0,0)) और ((-a,0)) / ((0,0)) and ((-a,0))
C ((a,0)) और ((-a,0)) / ((a,0)) and ((-a,0))
D ((0,a)) और ((a,0)) / ((0,a)) and ((a,0))
Explanation opens after your attempt
Correct Answer
A. ((0,0)) और ((a,0)) / ((0,0)) and ((a,0))
Step 1
Concept
(x-2 -ax=x(x-a)), so the zeroes are (0) and (a). Tip: factor out the common (x).
Step 2
Why this answer is correct
The correct answer is A. ((0,0)) और ((a,0)) / ((0,0)) and ((a,0)). (x-2 -ax=x(x-a)), so the zeroes are (0) and (a). Tip: factor out the common (x).
Step 3
Exam Tip
(x-2 -ax=x(x-a)), इसलिए शून्यक (0) और (a) हैं। टिप: सामान्य (x) गुणनखंड निकालें।
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Question
Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि किसी बहुपद के ग्राफ का (x)-अक्ष कटान ((0,0)) और ((a,0)) है, जहाँ \(a\neq0\), तो शून्यकों का गुणनफल क्या होगा?
If a polynomial graph has (x)-axis intersections ((0,0)) and ((a,0)), where \(a\neq0\), what will be the product of the zeroes?
#origin
#product of zeroes
#symbolic
A (a)
B (0)
C \(a^2\)
D (-a)
Explanation opens after your attempt
Step 1
Concept
The zeroes are (0) and (a), so the product is (0). Tip: if (0) is included, the product is (0).
Step 2
Why this answer is correct
The correct answer is B. (0). The zeroes are (0) and (a), so the product is (0). Tip: if (0) is included, the product is (0).
Step 3
Exam Tip
शून्यक (0) और (a) हैं, इसलिए गुणनफल (0) है। टिप: (0) शामिल हो तो गुणनफल (0) होगा।
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Question
Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि (p(x)=x-4 -1) है, तो ग्राफ के वास्तविक (x)-अक्ष कटान कौन से हैं?
If (p(x)=x-4 -1), what are the real (x)-axis intersections of the graph?
#quartic
#real zeroes
#graph
A ((-1,0)) और ((1,0)) / ((-1,0)) and ((1,0))
B ((-1,0)), ((0,0)), ((1,0))
C ((1,0)) और ((4,0)) / ((1,0)) and ((4,0))
D कोई नहीं / None
Explanation opens after your attempt
Correct Answer
A. ((-1,0)) और ((1,0)) / ((-1,0)) and ((1,0))
Step 1
Concept
(x-4 -1=\(x^2-1\)\(x^2+1\)), and the real zeroes are only \(\pm1\). Tip: \(x^2+1\) gives no real zero.
Step 2
Why this answer is correct
The correct answer is A. ((-1,0)) और ((1,0)) / ((-1,0)) and ((1,0)). (x-4 -1=\(x^2-1\)\(x^2+1\)), and the real zeroes are only \(\pm1\). Tip: \(x^2+1\) gives no real zero.
Step 3
Exam Tip
(x-4 -1=\(x^2-1\)\(x^2+1\)) है और वास्तविक शून्यक केवल \(\pm1\) हैं। टिप: \(x^2+1\) वास्तविक शून्यक नहीं देता।
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Question
Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि (p(x)=4x-2 -25) है, तो ग्राफ के (x)-अक्ष कटान कौन से हैं?
If (p(x)=4x-2 -25), what are the (x)-axis intersections of the graph?
#difference of squares
#fraction zeroes
#graph
A (\left\(\frac{5}{2},0\right\)) और (\left\(-\frac{5}{2},0\right\)) / (\left\(\frac{5}{2},0\right\)) and (\left\(-\frac{5}{2},0\right\))
B ((5,0)) और ((-5,0)) / ((5,0)) and ((-5,0))
C (\left\(\frac{2}{5},0\right\)) और (\left\(-\frac{2}{5},0\right\)) / (\left\(\frac{2}{5},0\right\)) and (\left\(-\frac{2}{5},0\right\)
D कोई नहीं / None
Explanation opens after your attempt
Correct Answer
A. (\left\(\frac{5}{2},0\right\)) और (\left\(-\frac{5}{2},0\right\)) / (\left\(\frac{5}{2},0\right\)) and (\left\(-\frac{5}{2},0\right\))
Step 1
Concept
From \(4x^2-25=0\), \(x=\pm\frac{5}{2}\). Tip: treat \(4x^2\) as ((2x)2 ).
Step 2
Why this answer is correct
The correct answer is A. (\left\(\frac{5}{2},0\right\)) और (\left\(-\frac{5}{2},0\right\)) / (\left\(\frac{5}{2},0\right\)) and (\left\(-\frac{5}{2},0\right\)). From \(4x^2-25=0\), \(x=\pm\frac{5}{2}\). Tip: treat \(4x^2\) as ((2x)2 ).
Step 3
Exam Tip
\(4x^2-25=0\) से \(x=\pm\frac{5}{2}\) मिलता है। टिप: \(4x^2\) को ((2x)2 ) समझें।
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Question
Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि (p(x)=x-2 -5x+k) का एक शून्यक (2) है, तो दूसरा शून्यक और (x)-अक्ष कटान क्या होगा?
If (p(x)=x-2 -5x+k) has one zero (2), what will be the other zero and the (x)-axis intersections?
#quadratic
#missing zero
#intercepts
A दूसरा (3), कटान ((2,0)), ((3,0)) / Other (3), intersections ((2,0)), ((3,0))
B दूसरा (-3), कटान ((2,0)), ((-3,0)) / Other (-3), intersections ((2,0)), ((-3,0))
C दूसरा (5), कटान ((2,0)), ((5,0)) / Other (5), intersections ((2,0)), ((5,0))
D दूसरा (0), कटान ((2,0)), ((0,0)) / Other (0), intersections ((2,0)), ((0,0))
Explanation opens after your attempt
Correct Answer
A. दूसरा (3), कटान ((2,0)), ((3,0)) / Other (3), intersections ((2,0)), ((3,0))
Step 1
Concept
In the quadratic, the sum of zeroes is (5), so the other zero is (3). Tip: immediately convert a zero to ((x,0)).
Step 2
Why this answer is correct
The correct answer is A. दूसरा (3), कटान ((2,0)), ((3,0)) / Other (3), intersections ((2,0)), ((3,0)). In the quadratic, the sum of zeroes is (5), so the other zero is (3). Tip: immediately convert a zero to ((x,0)).
Step 3
Exam Tip
द्विघात में शून्यकों का योग (5) है, इसलिए दूसरा शून्यक (3) है। टिप: शून्यक को तुरंत ((x,0)) में बदलें।
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Question
Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि किसी बहुपद के ग्राफ के (x)-अक्ष कटान ((r,0)), ((s,0)), ((t,0)) हैं, तो शून्यकों का योग क्या होगा?
If the (x)-axis intersections of a polynomial graph are ((r,0)), ((s,0)), ((t,0)), what will be the sum of the zeroes?
#symbolic zeroes
#sum
#coordinates
A (r+s+t)
B (rst)
C (0)
D (r-s+t)
Explanation opens after your attempt
Correct Answer
A. (r+s+t)
Step 1
Concept
The zeroes are the first coordinates (r), (s), (t). Tip: read the first coordinate even in symbolic points.
Step 2
Why this answer is correct
The correct answer is A. (r+s+t). The zeroes are the first coordinates (r), (s), (t). Tip: read the first coordinate even in symbolic points.
Step 3
Exam Tip
शून्यक पहले निर्देशांक (r), (s), (t) हैं। टिप: प्रतीकात्मक बिंदुओं में भी पहला निर्देशांक पढ़ें।
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Question
Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि (p(x)=x-2 +2x-15) है, तो ग्राफ के (x)-अक्ष कटान कौन से हैं?
If (p(x)=x-2 +2x-15), what are the (x)-axis intersections of the graph?
#quadratic factorization
#intercepts
#zeroes
A ((3,0)) और ((-5,0)) / ((3,0)) and ((-5,0))
B ((-3,0)) और ((5,0)) / ((-3,0)) and ((5,0))
C ((0,3)) और ((0,-5)) / ((0,3)) and ((0,-5))
D ((15,0)) और ((2,0)) / ((15,0)) and ((2,0))
Explanation opens after your attempt
Correct Answer
A. ((3,0)) और ((-5,0)) / ((3,0)) and ((-5,0))
Step 1
Concept
(x-2 +2x-15=(x+5)(x-3)), so the zeroes are (-5) and (3). Tip: form points ((x,0)) from factors.
Step 2
Why this answer is correct
The correct answer is A. ((3,0)) और ((-5,0)) / ((3,0)) and ((-5,0)). (x-2 +2x-15=(x+5)(x-3)), so the zeroes are (-5) and (3). Tip: form points ((x,0)) from factors.
Step 3
Exam Tip
(x-2 +2x-15=(x+5)(x-3)), इसलिए शून्यक (-5) और (3) हैं। टिप: गुणनखंडों से बिंदु ((x,0)) बनाएं।
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Question
Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि किसी परवलय के (x)-अक्ष कटान ((-7,0)) और ((1,0)) हैं, तो उसके शून्यकों के मध्यबिंदु का निर्देशांक क्या है?
If the (x)-axis intersections of a parabola are ((-7,0)) and ((1,0)), what is the coordinate of the midpoint of its zeroes?
#midpoint
#zeroes
#parabola
A ((-3,0))
B ((-4,0))
C ((3,0))
D ((0,-3))
Explanation opens after your attempt
Correct Answer
A. ((-3,0))
Step 1
Concept
The midpoint is (\left\(\frac{-7+1}{2},0\right\)=(-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\(\frac{-7+1}{2},0\right\)=(-3,0)). Tip: on the (x)-axis the midpoint has (y=0).
Step 3
Exam Tip
मध्यबिंदु (\left\(\frac{-7+1}{2},0\right\)=(-3,0)) है। टिप: (x)-अक्ष पर मध्यबिंदु का (y)-मान (0) रहता है।
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Question
Hard Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि (p(x)=x-2 -(a+b)x+ab) है, तो ग्राफ के (x)-अक्ष कटान कौन से होंगे?
If (p(x)=x-2 -(a+b)x+ab), what will be the (x)-axis intersections of the graph?
#symbolic factorization
#intercepts
#zeroes
A ((a,0)) और ((b,0)) / ((a,0)) and ((b,0))
B ((0,a)) और ((0,b)) / ((0,a)) and ((0,b))
C ((-a,0)) और ((-b,0)) / ((-a,0)) and ((-b,0))
D ((a,b)) और ((b,a)) / ((a,b)) and ((b,a))
Explanation opens after your attempt
Correct Answer
A. ((a,0)) और ((b,0)) / ((a,0)) and ((b,0))
Step 1
Concept
The polynomial equals ((x-a)(x-b)), so the zeroes are (a) and (b). Tip: connect factor form with graph intersections.
Step 2
Why this answer is correct
The correct answer is A. ((a,0)) और ((b,0)) / ((a,0)) and ((b,0)). The polynomial equals ((x-a)(x-b)), so the zeroes are (a) and (b). Tip: connect factor form with graph intersections.
Step 3
Exam Tip
बहुपद ((x-a)(x-b)) के बराबर है, इसलिए शून्यक (a) और (b) हैं। टिप: गुणनखंड रूप को ग्राफ कटान से जोड़ें।
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Question
Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि (p(x)=x-2 -3x-10) है तो ग्राफ के (x)-अक्ष कटान कौन से हैं?
If (p(x)=x-2 -3x-10), what are the (x)-axis intersections of the graph?
#quadratic factor graph
A ((5,0)) और ((-2,0)) / ((5,0)) and ((-2,0))
B ((-5,0)) और ((2,0)) / ((-5,0)) and ((2,0))
C ((0,5)) और ((0,-2)) / ((0,5)) and ((0,-2))
D ((10,0)) और ((-3,0)) / ((10,0)) and ((-3,0))
Explanation opens after your attempt
Correct Answer
A. ((5,0)) और ((-2,0)) / ((5,0)) and ((-2,0))
Step 1
Concept
(x-2 -3x-10=(x-5)(x+2)), so the zeroes are (5) and (-2). Tip: write intersection points from factors.
Step 2
Why this answer is correct
The correct answer is A. ((5,0)) और ((-2,0)) / ((5,0)) and ((-2,0)). (x-2 -3x-10=(x-5)(x+2)), so the zeroes are (5) and (-2). Tip: write intersection points from factors.
Step 3
Exam Tip
(x-2 -3x-10=(x-5)(x+2)) इसलिए शून्यक (5) और (-2) हैं। टिप: गुणनखंडों से कटान बिंदु लिखें।
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Question
Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि (p(x)=2(x-4)(x+1)) है तो बाहरी गुणक (2) ग्राफ के (x)-अक्ष कटानों को कैसे प्रभावित करता है?
If (p(x)=2(x-4)(x+1)), how does the outside multiplier (2) affect the (x)-axis intersections of the graph?
#constant multiplier graph
A कटान (2) से गुणा हो जाते हैं / The intersections get multiplied by (2)
B कटान नहीं बदलते / The intersections do not change
C एक नया कटान (x=2) जुड़ता है / A new intersection (x=2) is added
D सभी कटान हट जाते हैं / All intersections disappear
Explanation opens after your attempt
Correct Answer
B. कटान नहीं बदलते / The intersections do not change
Step 1
Concept
A non-zero constant multiplier does not change zeroes. Tip: zeroes come from factors that make the value zero.
Step 2
Why this answer is correct
The correct answer is B. कटान नहीं बदलते / The intersections do not change. A non-zero constant multiplier does not change zeroes. Tip: zeroes come from factors that make the value zero.
Step 3
Exam Tip
अशून्य स्थिर गुणक शून्यकों को नहीं बदलता। टिप: शून्यक केवल शून्य बनाने वाले कारकों से मिलते हैं।
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Question
Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
किसी परवलय के (x)-अक्ष कटान ((1,0)) और ((7,0)) हैं। उसका सममिति अक्ष किस (x)-मान से गुजर सकता है?
The (x)-axis intersections of a parabola are ((1,0)) and ((7,0)). Through which (x)-value can its axis of symmetry pass?
#axis of symmetry zeroes
A (x=3)
B (x=4)
C (x=6)
D (x=8)
Explanation opens after your attempt
Step 1
Concept
The axis of symmetry passes through the average \(x=\frac{1+7}{2}=4\). Tip: the middle of two zeroes is useful in a parabola.
Step 2
Why this answer is correct
The correct answer is B. (x=4). The axis of symmetry passes through the average \(x=\frac{1+7}{2}=4\). Tip: the middle of two zeroes is useful in a parabola.
Step 3
Exam Tip
सममिति अक्ष शून्यकों के औसत \(x=\frac{1+7}{2}=4\) से गुजरता है। टिप: परवलय में दो शून्यकों का मध्य उपयोगी है।
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Question
Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
यदि (p(-3)=0), (p(2)=5) और (p(8)=0) है तो ग्राफ के (x)-अक्ष कटान कौन से होंगे?
If (p(-3)=0), (p(2)=5) and (p(8)=0), what will be the (x)-axis intersections of the graph?
#function values zeroes
A ((-3,0)) और ((8,0)) / ((-3,0)) and ((8,0))
B ((2,5)) और ((8,0)) / ((2,5)) and ((8,0))
C ((0,-3)) और ((0,8)) / ((0,-3)) and ((0,8))
D ((-3,5)) और ((2,0)) / ((-3,5)) and ((2,0))
Explanation opens after your attempt
Correct Answer
A. ((-3,0)) और ((8,0)) / ((-3,0)) and ((8,0))
Step 1
Concept
An (x)-axis intersection occurs where (p(x)=0). Tip: (p(2)=5) does not give a zero.
Step 2
Why this answer is correct
The correct answer is A. ((-3,0)) और ((8,0)) / ((-3,0)) and ((8,0)). An (x)-axis intersection occurs where (p(x)=0). Tip: (p(2)=5) does not give a zero.
Step 3
Exam Tip
जहाँ (p(x)=0) है वहीं (x)-अक्ष कटान होता है। टिप: (p(2)=5) शून्यक नहीं देता।
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Question
Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि किसी ग्राफ के (x)-अक्ष कटान ((3,0)) और ((12,0)) हैं तो शून्यकों का औसत क्या है?
If the (x)-axis intersections of a graph are ((3,0)) and ((12,0)), what is the average of the zeroes?
#average zeroes intercepts
A (15)
B (9)
C (7.5)
D (36)
Explanation opens after your attempt
Step 1
Concept
The average is \(\frac{3+12}{2}=7.5\). Tip: divide the sum by (2) for the average.
Step 2
Why this answer is correct
The correct answer is C. (7.5). The average is \(\frac{3+12}{2}=7.5\). Tip: divide the sum by (2) for the average.
Step 3
Exam Tip
औसत \(\frac{3+12}{2}=7.5\) है। टिप: औसत में योग को (2) से भाग दें।
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Question
Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(x)=x-2 -7x+12) है तो ग्राफ के (x)-अक्ष कटान कौन से हैं?
If (p(x)=x-2 -7x+12), what are the (x)-axis intersections of the graph?
#quadratic factor intercepts
A ((3,0)) और ((4,0)) / ((3,0)) and ((4,0))
B ((-3,0)) और ((-4,0)) / ((-3,0)) and ((-4,0))
C ((0,3)) और ((0,4)) / ((0,3)) and ((0,4))
D ((7,0)) और ((12,0)) / ((7,0)) and ((12,0))
Explanation opens after your attempt
Correct Answer
A. ((3,0)) और ((4,0)) / ((3,0)) and ((4,0))
Step 1
Concept
(x-2 -7x+12=(x-3)(x-4)), so the zeroes are (3) and (4). Tip: factor and then write intersection points.
Step 2
Why this answer is correct
The correct answer is A. ((3,0)) और ((4,0)) / ((3,0)) and ((4,0)). (x-2 -7x+12=(x-3)(x-4)), so the zeroes are (3) and (4). Tip: factor and then write intersection points.
Step 3
Exam Tip
(x-2 -7x+12=(x-3)(x-4)) इसलिए शून्यक (3) और (4) हैं। टिप: गुणनखंड बनाकर कटान बिंदु लिखें।
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Question
Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि (p(2)=0), (p(5)=0) और (p(9)=0), तो ग्राफ पर (x)-अक्ष कटान कितने अलग होंगे?
If (p(2)=0), (p(5)=0) and (p(9)=0), how many distinct (x)-axis intersections will be on the graph?
#function zero count
A एक / One
B दो / Two
C तीन / Three
D नौ / Nine
Explanation opens after your attempt
Correct Answer
C. तीन / Three
Step 1
Concept
Three distinct (x)-values give three distinct (x)-axis points. Tip: (p(a)=0) gives ((a,0)).
Step 2
Why this answer is correct
The correct answer is C. तीन / Three. Three distinct (x)-values give three distinct (x)-axis points. Tip: (p(a)=0) gives ((a,0)).
Step 3
Exam Tip
तीन अलग (x)-मान तीन अलग (x)-अक्ष बिंदु देते हैं। टिप: (p(a)=0) से ((a,0)) मिलता है।
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Question
Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
किसी आलेख में (x)-अक्ष कटान (x=2) और (x=10) हैं। दोनों शून्यकों के बीच दूरी कितनी है?
A graph has (x)-axis intersections at (x=2) and (x=10). What is the distance between the two zeroes?
#distance zeroes number line
A (8)
B (12)
C (20)
D (5)
Explanation opens after your attempt
Step 1
Concept
The distance is (10-2=8). Tip: distance is always measured positive.
Step 2
Why this answer is correct
The correct answer is A. (8). The distance is (10-2=8). Tip: distance is always measured positive.
Step 3
Exam Tip
दूरी (10-2=8) है। टिप: दूरी हमेशा धनात्मक मापी जाती है।
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Question
Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 23
यदि किसी आलेख के (x)-अक्ष कटान ((-8,0)) और ((3,0)) हैं तो शून्यकों का सही जोड़ा कौन सा है?
If the (x)-axis intersections of a graph are ((-8,0)) and ((3,0)), which is the correct pair of zeroes?
#intercepts zeroes coordinates
A ((0,-8)) और ((0,3)) / ((0,-8)) and ((0,3))
B (-8) और (3) / (-8) and (3)
C (8) और (-3) / (8) and (-3)
D (-8) और (0) / (-8) and (0)
Explanation opens after your attempt
Correct Answer
B. (-8) और (3) / (-8) and (3)
Step 1
Concept
The first coordinates of intersection points are the zeroes. Tip: choose points whose second coordinate is (0).
Step 2
Why this answer is correct
The correct answer is B. (-8) और (3) / (-8) and (3). The first coordinates of intersection points are the zeroes. Tip: choose points whose second coordinate is (0).
Step 3
Exam Tip
कटान बिंदुओं के पहले निर्देशांक शून्यक होते हैं। टिप: दूसरे निर्देशांक को (0) देखकर बिंदु चुनें।
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Question
Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
किसी ग्राफ में (x)-अक्ष कटान ((a,0)), ((b,0)), ((c,0)) हैं। इनमें से कौन सा कथन सही है?
A graph has (x)-axis intersections ((a,0)), ((b,0)), ((c,0)). Which statement is correct?
#general graph rule
#zeroes
#intercepts
A शून्यक (0,0,0) हैं / The zeroes are (0,0,0)
B शून्यक (a,b,c) हैं / The zeroes are (a,b,c)
C शून्यक (a+0,b+0,c+0) नहीं लिखे जा सकते / The zeroes cannot be written as (a+0,b+0,c+0)
D केवल (c) शून्यक है / Only (c) is a zero
Explanation opens after your attempt
Correct Answer
B. शून्यक (a,b,c) हैं / The zeroes are (a,b,c)
Step 1
Concept
The first coordinate of each intersection point is a zero. Tip: read the zero (a) from ((a,0)).
Step 2
Why this answer is correct
The correct answer is B. शून्यक (a,b,c) हैं / The zeroes are (a,b,c). The first coordinate of each intersection point is a zero. Tip: read the zero (a) from ((a,0)).
Step 3
Exam Tip
हर कटान बिंदु का पहला निर्देशांक शून्यक है। टिप: ((a,0)) से शून्यक (a) पढ़ें।
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Question
Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
किसी परवलय के (x)-अक्ष कटान ((r,0)) और ((s,0)) हैं। इसके शून्यकों का औसत क्या होगा?
The (x)-axis intersections of a parabola are ((r,0)) and ((s,0)). What is the average of its zeroes?
#average of zeroes
#parabola
#graph
A (rs)
B (r+s)
C \(\frac{r+s}{2}\)
D \(\frac{r-s}{2}\)
Explanation opens after your attempt
Correct Answer
C. \(\frac{r+s}{2}\)
Step 1
Concept
The zeroes are (r) and (s), so the average is \(\frac{r+s}{2}\). Tip: divide the sum by the number of values.
Step 2
Why this answer is correct
The correct answer is C. \(\frac{r+s}{2}\). The zeroes are (r) and (s), so the average is \(\frac{r+s}{2}\). Tip: divide the sum by the number of values.
Step 3
Exam Tip
शून्यक (r) और (s) हैं, इसलिए औसत \(\frac{r+s}{2}\) है। टिप: औसत में योग को संख्या से भाग दें।
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Question
Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि किसी ग्राफ के (x)-अक्ष कटान ((m,0)) और ((n,0)) हैं, तो शून्यकों का गुणनफल क्या होगा?
If the (x)-axis intersections of a graph are ((m,0)) and ((n,0)), what is the product of the zeroes?
#general rule
#product
#zeroes
A (m+n)
B (mn)
C (0)
D (m-n)
Explanation opens after your attempt
Step 1
Concept
The zeroes are (m) and (n), so the product is (mn). Tip: the first coordinate of the intersection point is the zero.
Step 2
Why this answer is correct
The correct answer is B. (mn). The zeroes are (m) and (n), so the product is (mn). Tip: the first coordinate of the intersection point is the zero.
Step 3
Exam Tip
शून्यक (m) और (n) हैं, इसलिए गुणनफल (mn) है। टिप: कटान बिंदु का पहला निर्देशांक ही शून्यक है।
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Question
Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि (p(x)=x-2 -16), तो इसके ग्राफ के (x)-अक्ष कटान कौन से हैं?
If (p(x)=x-2 -16), what are the (x)-axis intersections of its graph?
#quadratic
#intercepts
#zeroes
A ((0,16)) और ((16,0)) / ((0,16)) and ((16,0))
B ((4,0)) और ((-4,0)) / ((4,0)) and ((-4,0))
C ((8,0)) और ((-8,0)) / ((8,0)) and ((-8,0))
D कोई नहीं / None
Explanation opens after your attempt
Correct Answer
B. ((4,0)) और ((-4,0)) / ((4,0)) and ((-4,0))
Step 1
Concept
Solving \(x^2-16=0\) gives \(x=\pm4\). Tip: write zeroes as (x)-axis points.
Step 2
Why this answer is correct
The correct answer is B. ((4,0)) और ((-4,0)) / ((4,0)) and ((-4,0)). Solving \(x^2-16=0\) gives \(x=\pm4\). Tip: write zeroes as (x)-axis points.
Step 3
Exam Tip
\(x^2-16=0\) से \(x=\pm4\) मिलता है। टिप: शून्यक को (x)-अक्ष बिंदु में लिखें।
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Question
Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
यदि किसी परवलय के (x)-अक्ष कटान ((-1,0)) और ((4,0)) हैं, तो शून्यकों का योग क्या है?
If the (x)-axis intersections of a parabola are ((-1,0)) and ((4,0)), what is the sum of zeroes?
#sum of zeroes
#graph
#parabola
A (3)
B (-3)
C (4)
D (-4)
Explanation opens after your attempt
Step 1
Concept
The zeroes are (-1) and (4), so their sum is (3). Tip: first read the (x)-values from the points.
Step 2
Why this answer is correct
The correct answer is A. (3). The zeroes are (-1) and (4), so their sum is (3). Tip: first read the (x)-values from the points.
Step 3
Exam Tip
शून्यक (-1) और (4) हैं, इसलिए योग (3) है। टिप: पहले बिंदुओं से (x)-मान पढ़ें।
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Question
Medium Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
बहुपद (p(x)=(x-4)(x+2)) के आलेख के (x)-अक्ष कटान कौन से होंगे?
What will be the (x)-axis intersections of the graph of (p(x)=(x-4)(x+2))?
#factor form
#graph
#zeroes
A ((4,0)) और ((-2,0)) / ((4,0)) and ((-2,0))
B ((-4,0)) और ((2,0)) / ((-4,0)) and ((2,0))
C ((0,4)) और ((0,-2)) / ((0,4)) and ((0,-2))
D ((4,-2)) और ((-2,4)) / ((4,-2)) and ((-2,4))
Explanation opens after your attempt
Correct Answer
A. ((4,0)) और ((-2,0)) / ((4,0)) and ((-2,0))
Step 1
Concept
Setting the factors to zero gives (x=4) and (x=-2). Tip: convert each zero into the point ((x,0)).
Step 2
Why this answer is correct
The correct answer is A. ((4,0)) और ((-2,0)) / ((4,0)) and ((-2,0)). Setting the factors to zero gives (x=4) and (x=-2). Tip: convert each zero into the point ((x,0)).
Step 3
Exam Tip
कारकों को शून्य करने पर (x=4) और (x=-2) मिलते हैं। टिप: शून्यक को ((x,0)) बिंदु में बदलें।
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Easy Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
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
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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Question
Easy Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 24
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
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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Question
Easy Mathematics
Chapter 2: Polynomials Geometrical meaning of the zeroes of a polynomial. Class 10 Level 22
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
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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