100 results found for "fractional-zeroes" in Class 10.
यदि परवलय के शून्यक (-4) और (10) हैं तथा वह नीचे की ओर खुलता है तो शून्यकों के बाहर ग्राफ कहाँ होगा?
If a parabola has zeroes (-4) and (10) and opens downward, where will the graph be outside the zeroes?
#downward parabola
#sign outside zeroes
#graph
A (x)-अक्ष के ऊपर / Above the (x)-axis
B (x)-अक्ष के नीचे / Below the (x)-axis
C ठीक (x)-अक्ष पर / Exactly on the (x)-axis
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Correct Answer
B. (x)-अक्ष के नीचे / Below the (x)-axis
Step 1
Concept
For a downward-opening parabola, values outside the zeroes are negative. Tip: opening direction changes sign regions.
Step 2
Why this answer is correct
The correct answer is B. (x)-अक्ष के नीचे / Below the (x)-axis. For a downward-opening parabola, values outside the zeroes are negative. Tip: opening direction changes sign regions.
Step 3
Exam Tip
नीचे खुलने वाले परवलय में शून्यकों के बाहर मान ऋणात्मक होते हैं। टिप: खुलने की दिशा संकेत क्षेत्र बदलती है।
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यदि परवलय के शून्यक (-2) और (8) हैं तथा वह नीचे की ओर खुलता है, तो शून्यकों के बाहर ग्राफ कहाँ होगा?
If a parabola has zeroes (-2) and (8) and opens downward, where will the graph be outside the zeroes?
#downward parabola
#sign outside zeroes
#graph
A (x)-अक्ष के ऊपर / Above the (x)-axis
B (x)-अक्ष के नीचे / Below the (x)-axis
C ठीक (x)-अक्ष पर / Exactly on the (x)-axis
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Correct Answer
B. (x)-अक्ष के नीचे / Below the (x)-axis
Step 1
Concept
For a downward-opening parabola, values outside the zeroes are negative. Tip: opening direction changes sign regions.
Step 2
Why this answer is correct
The correct answer is B. (x)-अक्ष के नीचे / Below the (x)-axis. For a downward-opening parabola, values outside the zeroes are negative. Tip: opening direction changes sign regions.
Step 3
Exam Tip
नीचे खुलने वाले परवलय में शून्यकों के बाहर मान ऋणात्मक होते हैं। टिप: खुलने की दिशा संकेत क्षेत्र बदलती है।
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यदि किसी परवलय के शून्यक (-1) और (7) हैं तथा वह नीचे की ओर खुलता है, तो शून्यकों के बाहर ग्राफ कहाँ होगा?
If a parabola has zeroes (-1) and (7) and opens downward, where will the graph be outside the zeroes?
#parabola
#sign outside zeroes
#graph
A (x)-अक्ष के ऊपर / Above the (x)-axis
B (x)-अक्ष के नीचे / Below the (x)-axis
C ठीक (x)-अक्ष पर / Exactly on the (x)-axis
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Correct Answer
B. (x)-अक्ष के नीचे / Below the (x)-axis
Step 1
Concept
For a downward-opening parabola, values outside the zeroes are negative. Tip: when the direction changes, sign regions also change.
Step 2
Why this answer is correct
The correct answer is B. (x)-अक्ष के नीचे / Below the (x)-axis. For a downward-opening parabola, values outside the zeroes are negative. Tip: when the direction changes, sign regions also change.
Step 3
Exam Tip
नीचे खुलने वाले परवलय में शून्यकों के बाहर मान ऋणात्मक होते हैं। टिप: दिशा बदलने पर संकेत क्षेत्र भी बदलता है।
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यदि किसी बहुपद के वास्तविक शून्यक (5), (5), (-1) हैं तो अलग वास्तविक शून्यक कौन से हैं?
If the real zeroes of a polynomial are (5), (5), (-1), what are the distinct real zeroes?
#distinct repeated values
A (5) और (-1) / (5) and (-1)
B केवल (5) / Only (5)
C (5), (5), (-1)
D केवल (-1) / Only (-1)
Explanation opens after your attempt
Correct Answer
A. (5) और (-1) / (5) and (-1)
Step 1
Concept
The repeated (5) is counted only once among distinct zeroes. Tip: make a list of distinct values.
Step 2
Why this answer is correct
The correct answer is A. (5) और (-1) / (5) and (-1). The repeated (5) is counted only once among distinct zeroes. Tip: make a list of distinct values.
Step 3
Exam Tip
दोहराया (5) अलग शून्यक में एक बार ही गिना जाता है। टिप: अलग मानों की सूची बनाएं।
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यदि किसी बहुपद के वास्तविक शून्यक (2), (2) और (-5) लिखे हैं, तो अलग वास्तविक शून्यक कौन से हैं?
If the real zeroes of a polynomial are written as (2), (2) and (-5), what are the distinct real zeroes?
#repeated distinct zeroes
A (2) और (-5) / (2) and (-5)
B केवल (2) / Only (2)
C (2), (2), (-5)
D केवल (-5) / Only (-5)
Explanation opens after your attempt
Correct Answer
A. (2) और (-5) / (2) and (-5)
Step 1
Concept
The repeated (2) is counted once for distinct zeroes. Tip: do not rewrite the same value for distinct zeroes.
Step 2
Why this answer is correct
The correct answer is A. (2) और (-5) / (2) and (-5). The repeated (2) is counted once for distinct zeroes. Tip: do not rewrite the same value for distinct zeroes.
Step 3
Exam Tip
दोहराया (2) अलग शून्यक में एक बार गिना जाता है। टिप: अलग शून्यक में समान मान पुनः न लिखें।
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कौन सा व्यंजक बहुपद नहीं है क्योंकि चर की घात भिन्न है?
Which expression is not a polynomial because the variable has a fractional power?
#not polynomial
#fractional power
#definition
A \(x^4-2x+5\)
B \(3x^2+\sqrt{2}x-7\)
C \(x^{\frac{3}{2}}+x+1\)
D \(9x^3-4x^2\)
Explanation opens after your attempt
Correct Answer
C. \(x^{\frac{3}{2}}+x+1\)
Step 1
Concept
In \(x^{\frac{3}{2}}\), the power of the variable is fractional, so it is not a polynomial. In a polynomial, powers are non-negative integers.
Step 2
Why this answer is correct
The correct answer is C. \(x^{\frac{3}{2}}+x+1\). In \(x^{\frac{3}{2}}\), the power of the variable is fractional, so it is not a polynomial. In a polynomial, powers are non-negative integers.
Step 3
Exam Tip
\(x^{\frac{3}{2}}\) में चर की घात भिन्न है, इसलिए यह बहुपद नहीं है। बहुपद में घातें अऋणात्मक पूर्णांक होती हैं।
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यदि (p(x)=x-2 -6x+8), तो शून्यकों के वर्गों से बना मोनिक बहुपद कौन-सा है?
If (p(x)=x-2 -6x+8), which monic polynomial has the squares of its zeroes as zeroes?
#transformed-zeroes
#squares
#quadratic
A \(x^2-20x+64\)
B \(x^2-6x+8\)
C \(x^2-12x+16\)
D \(x^2-16x+64\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-20x+64\)
Step 1
Concept
The original zeroes are (2) and (4), so the new zeroes are (4) and (16). The new polynomial is \(x^2-20x+64\).
Step 2
Why this answer is correct
The correct answer is A. \(x^2-20x+64\). The original zeroes are (2) and (4), so the new zeroes are (4) and (16). The new polynomial is \(x^2-20x+64\).
Step 3
Exam Tip
मूल शून्यक (2) और (4) हैं, इसलिए नए शून्यक (4) और (16) हैं। नया बहुपद \(x^2-20x+64\) है।
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यदि \(3+\sqrt{2}\) और \(3-\sqrt{2}\) किसी बहुपद के शून्यक हैं, तो शून्यकों का योग क्या है?
If \(3+\sqrt{2}\) and \(3-\sqrt{2}\) are zeroes of a polynomial, what is the sum of the zeroes?
#sum-of-zeroes
#conjugates
#polynomials
A (6)
B \(2\sqrt{2}\)
C (3)
D (9-2)
Explanation opens after your attempt
Step 1
Concept
The sum is (\(3+\sqrt{2}\)+\(3-\sqrt{2}\)=6). In exams the sum of conjugate zeroes is always rational.
Step 2
Why this answer is correct
The correct answer is A. (6). The sum is (\(3+\sqrt{2}\)+\(3-\sqrt{2}\)=6). In exams the sum of conjugate zeroes is always rational.
Step 3
Exam Tip
योग (\(3+\sqrt{2}\)+\(3-\sqrt{2}\)=6) है। परीक्षा में संयुग्मी शून्यकों का योग हमेशा परिमेय होता है।
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किस बहुपद में शून्यकों का योग परिमेय है लेकिन दोनों शून्यक अपरिमेय हैं?
Which polynomial has a rational sum of zeroes but both zeroes are irrational?
#rational-sum
#irrational-zeroes
#concept
A \(x^2-4x+1\)
B \(x^2-4x+4\)
C \(x^2+1\)
D \(x^2-5x+6\)
Explanation opens after your attempt
Correct Answer
A. \(x^2-4x+1\)
Step 1
Concept
In \(x^2-4x+1\), the sum is (4) and (D=16-4=12), so the zeroes are irrational. A rational sum does not mean rational zeroes.
Step 2
Why this answer is correct
The correct answer is A. \(x^2-4x+1\). In \(x^2-4x+1\), the sum is (4) and (D=16-4=12), so the zeroes are irrational. A rational sum does not mean rational zeroes.
Step 3
Exam Tip
\(x^2-4x+1\) में योग (4) है और (D=16-4=12) से शून्यक अपरिमेय हैं। परिमेय योग का अर्थ परिमेय शून्यक होना नहीं है।
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किस बहुपद के शून्यक वास्तविक हैं लेकिन परिमेय नहीं हैं?
Which polynomial has real zeroes but not rational zeroes?
#real-irrational-zeroes
#identification
#mcq
A \(x^2-9\)
B \(x^2+9\)
C \(x^2-8\)
D \(x^2-6x+9\)
Explanation opens after your attempt
Correct Answer
C. \(x^2-8\)
Step 1
Concept
From \(x^2-8=0\), \(x=\pm2\sqrt{2}\), which are irrational real. Check both perfect-square status and positivity.
Step 2
Why this answer is correct
The correct answer is C. \(x^2-8\). From \(x^2-8=0\), \(x=\pm2\sqrt{2}\), which are irrational real. Check both perfect-square status and positivity.
Step 3
Exam Tip
\(x^2-8=0\) से \(x=\pm2\sqrt{2}\), जो अपरिमेय वास्तविक हैं। पूर्ण वर्ग और धनात्मकता दोनों जाँचें।
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यदि \(\sqrt{2}\) और \(\sqrt{8}\) किसी द्विघात बहुपद के शून्यक हैं, तो शून्यकों का योग क्या है?
If \(\sqrt{2}\) and \(\sqrt{8}\) are zeroes of a quadratic polynomial, what is the sum of the zeroes?
#radical-simplification
#sum-of-zeroes
#irrational
A \(3\sqrt{2}\)
B \(2\sqrt{10}\)
C \(4\sqrt{2}\)
D \(\sqrt{10}\)
Explanation opens after your attempt
Correct Answer
A. \(3\sqrt{2}\)
Step 1
Concept
Since \(\sqrt{8}=2\sqrt{2}\), the sum is \(\sqrt{2}+2\sqrt{2}=3\sqrt{2}\). Simplify radicals first.
Step 2
Why this answer is correct
The correct answer is A. \(3\sqrt{2}\). Since \(\sqrt{8}=2\sqrt{2}\), the sum is \(\sqrt{2}+2\sqrt{2}=3\sqrt{2}\). Simplify radicals first.
Step 3
Exam Tip
क्योंकि \(\sqrt{8}=2\sqrt{2}\), योग \(\sqrt{2}+2\sqrt{2}=3\sqrt{2}\) है। पहले करणी को सरल करें।
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किसी बहुपद का ग्राफ (x)-अक्ष को केवल सम संख्याओं (-4), (2), और (8) पर काटता है। शून्यकों की संख्या क्या है?
A polynomial graph cuts the (x)-axis only at the even numbers (-4), (2), and (8). What is the number of zeroes?
#counting-zeroes
#graph
#integer-zeroes
A तीन / Three
B दो / Two
C छह / Six
D एक / One
Explanation opens after your attempt
Correct Answer
A. तीन / Three
Step 1
Concept
Three distinct (x)-intercepts give three zeroes. Count by intersections not by the type of numbers.
Step 2
Why this answer is correct
The correct answer is A. तीन / Three. Three distinct (x)-intercepts give three zeroes. Count by intersections not by the type of numbers.
Step 3
Exam Tip
तीन अलग (x)-प्रतिच्छेद तीन शून्यक देते हैं। संख्या के प्रकार से नहीं बल्कि प्रतिच्छेदों से गिनें।
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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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यदि परवलय नीचे की ओर खुलता है और (x)-अक्ष को दो बिंदुओं पर काटता है तो वास्तविक शून्यकों की संख्या क्या होगी?
If a parabola opens downward and cuts the (x)-axis at two points, how many real zeroes will it have?
#parabola
#downward
#real-zeroes
A दो / Two
B एक / One
C शून्य / Zero
D चार / Four
Explanation opens after your attempt
Step 1
Concept
The opening direction alone does not decide the number of zeroes. Two intersections clearly give two real zeroes.
Step 2
Why this answer is correct
The correct answer is A. दो / Two. The opening direction alone does not decide the number of zeroes. Two intersections clearly give two real zeroes.
Step 3
Exam Tip
खुलने की दिशा शून्यकों की संख्या अकेले तय नहीं करती। दो कटान स्पष्ट रूप से दो वास्तविक शून्यक देते हैं।
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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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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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यदि द्विघात ग्राफ (x)-अक्ष को दो अलग बिंदुओं पर काटता है तो उसके वास्तविक शून्यक कैसे होंगे?
If a quadratic graph cuts the (x)-axis at two distinct points, what kind of real zeroes does it have?
#quadratic
#distinct-real-zeroes
#graph
A दो भिन्न वास्तविक शून्यक / Two distinct real zeroes
B दो समान वास्तविक शून्यक / Two equal real zeroes
C कोई वास्तविक शून्यक नहीं / No real zero
D एक ही शून्यक और एक काल्पनिक शून्यक / One zero and one imaginary zero
Explanation opens after your attempt
Correct Answer
A. दो भिन्न वास्तविक शून्यक / Two distinct real zeroes
Step 1
Concept
Two separate intersections give two distinct real zeroes. Different (x)-intercepts mean different zeroes.
Step 2
Why this answer is correct
The correct answer is A. दो भिन्न वास्तविक शून्यक / Two distinct real zeroes. Two separate intersections give two distinct real zeroes. Different (x)-intercepts mean different zeroes.
Step 3
Exam Tip
दो अलग कटान दो अलग वास्तविक शून्यक देते हैं। ग्राफ में अलग (x)-प्रतिच्छेद अलग शून्यक होते हैं।
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यदि किसी बहुपद के ग्राफ के (x)-प्रतिच्छेद ((-4,0)), ((1,0)), और ((6,0)) हैं तो शून्यकों का समुच्चय क्या है?
If the (x)-intercepts of a polynomial graph are ((-4,0)), ((1,0)), and ((6,0)), what is the set of zeroes?
#x-intercepts
#set-of-zeroes
#graph
A ({-4,1,6})
B ({0,1,6})
C ({-4,0,6})
D ({-4,1,0})
Explanation opens after your attempt
Correct Answer
A. ({-4,1,6})
Step 1
Concept
A zero is the (x)-coordinate of the intercept point. Do not write (y=0) as the zero.
Step 2
Why this answer is correct
The correct answer is A. ({-4,1,6}). A zero is the (x)-coordinate of the intercept point. Do not write (y=0) as the zero.
Step 3
Exam Tip
शून्यक प्रतिच्छेद बिंदु का (x)-निर्देशांक होता है। (y=0) को शून्यक न लिखें।
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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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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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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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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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यदि (p(-12)=0), (p(-2)=6), (p(4)=0), (p(15)=0) है, तो कितने दिए गए (x)-मान शून्यक हैं?
If (p(-12)=0), (p(-2)=6), (p(4)=0), (p(15)=0), how many of the given (x)-values are zeroes?
#function table
#count zeroes
#graph
A दो / Two
B तीन / Three
C चार / Four
D एक / One
Explanation opens after your attempt
Correct Answer
B. तीन / Three
Step 1
Concept
The function value is (0) at (-12), (4), and (15). Tip: do not treat (p(-2)=6) as a zero.
Step 2
Why this answer is correct
The correct answer is B. तीन / Three. The function value is (0) at (-12), (4), and (15). Tip: do not treat (p(-2)=6) as a zero.
Step 3
Exam Tip
(-12), (4), (15) पर फलन मान (0) है। टिप: (p(-2)=6) को शून्यक न मानें।
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यदि नीचे खुलने वाले परवलय के शून्यक (-5) और (13) हैं, तो (x=2) पर ग्राफ कहाँ होगा?
If a downward-opening parabola has zeroes (-5) and (13), where will the graph be at (x=2)?
#downward parabola
#sign inside zeroes
#graph
A (x)-अक्ष के ऊपर / Above the (x)-axis
B (x)-अक्ष के नीचे / Below the (x)-axis
C ठीक (x)-अक्ष पर / Exactly 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
For a downward-opening parabola, values between the two zeroes are positive. Tip: (x=2) lies between the zeroes.
Step 2
Why this answer is correct
The correct answer is A. (x)-अक्ष के ऊपर / Above the (x)-axis. For a downward-opening parabola, values between the two zeroes are positive. Tip: (x=2) lies between the zeroes.
Step 3
Exam Tip
नीचे खुलने वाले परवलय में दो शून्यकों के बीच मान धनात्मक होते हैं। टिप: (x=2) दोनों शून्यकों के बीच है।
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यदि (p(x)=x-2 -19x+90) है, तो ग्राफ के शून्यकों के बीच दूरी कितनी है?
If (p(x)=x-2 -19x+90), what is the distance between the zeroes of the graph?
#distance between zeroes
#quadratic
#graph
A (1)
B (9)
C (19)
D (90)
Explanation opens after your attempt
Step 1
Concept
(x-2 -19x+90=(x-9)(x-10)), so the distance is (10-9=1). Tip: find zeroes first and then take distance.
Step 2
Why this answer is correct
The correct answer is A. (1). (x-2 -19x+90=(x-9)(x-10)), so the distance is (10-9=1). Tip: find zeroes first and then take distance.
Step 3
Exam Tip
(x-2 -19x+90=(x-9)(x-10)) है, इसलिए दूरी (10-9=1) है। टिप: पहले शून्यक निकालें फिर दूरी लें।
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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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यदि ग्राफ (x=-12) और (x=12) पर (x)-अक्ष को काटता है, तो शून्यकों का गुणनफल और योग क्या है?
If a graph cuts the (x)-axis at (x=-12) and (x=12), what are the product and sum of the zeroes?
#opposite zeroes
#product
#sum
A गुणनफल (-144), योग (0) / Product (-144), sum (0)
B गुणनफल (144), योग (0) / Product (144), sum (0)
C गुणनफल (0), योग (24) / Product (0), sum (24)
D गुणनफल (-24), योग (144) / Product (-24), sum (144)
Explanation opens after your attempt
Correct Answer
A. गुणनफल (-144), योग (0) / Product (-144), sum (0)
Step 1
Concept
The zeroes are (-12) and (12), so the product is (-144) and the sum is (0). Tip: opposite zeroes have sum (0).
Step 2
Why this answer is correct
The correct answer is A. गुणनफल (-144), योग (0) / Product (-144), sum (0). The zeroes are (-12) and (12), so the product is (-144) and the sum is (0). Tip: opposite zeroes have sum (0).
Step 3
Exam Tip
शून्यक (-12) और (12) हैं, इसलिए गुणनफल (-144) और योग (0) है। टिप: विपरीत शून्यकों का योग (0) होता है।
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यदि परवलय के शून्यक (q-11) और (q+7) हैं, तो सममिति अक्ष कौन सा होगा?
If the zeroes of a parabola are (q-11) and (q+7), what will be its axis of symmetry?
#symbolic zeroes
#axis symmetry
#parabola
A (x=q-2)
B (x=q+2)
C (x=2q-4)
D (x=q-4)
Explanation opens after your attempt
Correct Answer
A. (x=q-2)
Step 1
Concept
The axis of symmetry is at the average of the zeroes, (\frac{(q-11)+(q+7)}{2}=q-2). Tip: take the midpoint even with symbols.
Step 2
Why this answer is correct
The correct answer is A. (x=q-2). The axis of symmetry is at the average of the zeroes, (\frac{(q-11)+(q+7)}{2}=q-2). Tip: take the midpoint even with symbols.
Step 3
Exam Tip
सममिति अक्ष शून्यकों के औसत पर है, (\frac{(q-11)+(q+7)}{2}=q-2)। टिप: प्रतीकों में भी मध्य मान लें।
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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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यदि ग्राफ (x=-18), (x=-6), (x=5) और (x=13) पर (x)-अक्ष को काटता है, तो शून्यकों की परास क्या है?
If a graph cuts the (x)-axis at (x=-18), (x=-6), (x=5), and (x=13), what is the range of the zeroes?
#range of zeroes
#number line
#graph
A (19)
B (25)
C (31)
D (-31)
Explanation opens after your attempt
Step 1
Concept
The range is the difference between the greatest and smallest zero, (13-(-18)=31). Tip: range is always non-negative.
Step 2
Why this answer is correct
The correct answer is C. (31). The range is the difference between the greatest and smallest zero, (13-(-18)=31). Tip: range is always non-negative.
Step 3
Exam Tip
परास सबसे बड़े और सबसे छोटे शून्यक का अंतर है (13-(-18)=31)। टिप: परास हमेशा गैरऋणात्मक होती है।
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यदि (p(x)=(x-c)5 (x+d)2 ), जहाँ \(c\neq -d\), तो अलग शून्यक कौन से हैं?
If (p(x)=(x-c)5 (x+d)2 ), where \(c\neq -d\), what are the distinct zeroes?
#symbolic factors
#distinct zeroes
#multiplicity
A (c) और (-d) / (c) and (-d)
B (-c) और (d) / (-c) and (d)
C (c), (-d), (-d)
D केवल (c) / Only (c)
Explanation opens after your attempt
Correct Answer
A. (c) और (-d) / (c) and (-d)
Step 1
Concept
From (x-c=0) we get (c), and from (x+d=0) we get (-d). Tip: do not count repetition among distinct zeroes.
Step 2
Why this answer is correct
The correct answer is A. (c) और (-d) / (c) and (-d). From (x-c=0) we get (c), and from (x+d=0) we get (-d). Tip: do not count repetition among distinct zeroes.
Step 3
Exam Tip
(x-c=0) से (c) और (x+d=0) से (-d) मिलता है। टिप: अलग शून्यकों में दोहराव न गिनें।
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यदि (p(x)=(x+2)6 (x-5)2 ) है, तो अलग वास्तविक शून्यकों की संख्या और ग्राफ का व्यवहार क्या है?
If (p(x)=(x+2)6 (x-5)2 ), what are the number of distinct real zeroes and graph behavior?
#even multiplicity
#distinct zeroes
#tangent
A दो, दोनों पर स्पर्श / Two, touches at both
B दो, दोनों पर कटान / Two, crosses at both
C आठ, सभी पर स्पर्श / Eight, touches at all
D एक, केवल (x=-2) पर स्पर्श / One, touches only at (x=-2)
Explanation opens after your attempt
Correct Answer
A. दो, दोनों पर स्पर्श / Two, touches at both
Step 1
Concept
There are two distinct zeroes (-2) and (5), and both have even powers. Tip: at an even-power zero the graph usually touches.
Step 2
Why this answer is correct
The correct answer is A. दो, दोनों पर स्पर्श / Two, touches at both. There are two distinct zeroes (-2) and (5), and both have even powers. Tip: at an even-power zero the graph usually touches.
Step 3
Exam Tip
दो अलग शून्यक (-2) और (5) हैं तथा दोनों की घात सम है। टिप: सम घात वाले शून्यक पर ग्राफ सामान्यतः स्पर्श करता है।
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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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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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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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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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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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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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यदि (p(-10)=0), (p(-1)=4), (p(3)=0), (p(12)=0) है, तो कितने दिए गए (x)-मान शून्यक हैं?
If (p(-10)=0), (p(-1)=4), (p(3)=0), (p(12)=0), how many of the given (x)-values are zeroes?
#function table
#count zeroes
#graph
A दो / Two
B तीन / Three
C चार / Four
D एक / One
Explanation opens after your attempt
Correct Answer
B. तीन / Three
Step 1
Concept
The function value is (0) at (-10), (3), and (12). Tip: do not treat (p(-1)=4) as a zero.
Step 2
Why this answer is correct
The correct answer is B. तीन / Three. The function value is (0) at (-10), (3), and (12). Tip: do not treat (p(-1)=4) as a zero.
Step 3
Exam Tip
(-10), (3), (12) पर फलन मान (0) है। टिप: (p(-1)=4) को शून्यक न मानें।
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यदि नीचे खुलने वाले परवलय के शून्यक (-3) और (11) हैं, तो (x=4) पर ग्राफ कहाँ होगा?
If a downward-opening parabola has zeroes (-3) and (11), where will the graph be at (x=4)?
#downward parabola
#sign inside zeroes
#graph
A (x)-अक्ष के ऊपर / Above the (x)-axis
B (x)-अक्ष के नीचे / Below the (x)-axis
C ठीक (x)-अक्ष पर / Exactly 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
For a downward-opening parabola, values between the two zeroes are positive. Tip: (x=4) lies between the zeroes.
Step 2
Why this answer is correct
The correct answer is A. (x)-अक्ष के ऊपर / Above the (x)-axis. For a downward-opening parabola, values between the two zeroes are positive. Tip: (x=4) lies between the zeroes.
Step 3
Exam Tip
नीचे खुलने वाले परवलय में दो शून्यकों के बीच मान धनात्मक होते हैं। टिप: (x=4) दोनों शून्यकों के बीच है।
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यदि (p(x)=x-2 -17x+72) है, तो ग्राफ के शून्यकों के बीच दूरी कितनी है?
If (p(x)=x-2 -17x+72), what is the distance between the zeroes of the graph?
#distance between zeroes
#quadratic
#graph
A (1)
B (8)
C (17)
D (72)
Explanation opens after your attempt
Step 1
Concept
(x-2 -17x+72=(x-8)(x-9)), so the distance is (9-8=1). Tip: find zeroes first and then take distance.
Step 2
Why this answer is correct
The correct answer is A. (1). (x-2 -17x+72=(x-8)(x-9)), so the distance is (9-8=1). Tip: find zeroes first and then take distance.
Step 3
Exam Tip
(x-2 -17x+72=(x-8)(x-9)) है, इसलिए दूरी (9-8=1) है। टिप: पहले शून्यक निकालें फिर दूरी लें।
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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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यदि ग्राफ (x=-10) और (x=10) पर (x)-अक्ष को काटता है, तो शून्यकों का गुणनफल और योग क्या है?
If a graph cuts the (x)-axis at (x=-10) and (x=10), what are the product and sum of the zeroes?
#opposite zeroes
#product
#sum
A गुणनफल (-100), योग (0) / Product (-100), sum (0)
B गुणनफल (100), योग (0) / Product (100), sum (0)
C गुणनफल (0), योग (20) / Product (0), sum (20)
D गुणनफल (-20), योग (100) / Product (-20), sum (100)
Explanation opens after your attempt
Correct Answer
A. गुणनफल (-100), योग (0) / Product (-100), sum (0)
Step 1
Concept
The zeroes are (-10) and (10), so the product is (-100) and the sum is (0). Tip: opposite zeroes have sum (0).
Step 2
Why this answer is correct
The correct answer is A. गुणनफल (-100), योग (0) / Product (-100), sum (0). The zeroes are (-10) and (10), so the product is (-100) and the sum is (0). Tip: opposite zeroes have sum (0).
Step 3
Exam Tip
शून्यक (-10) और (10) हैं, इसलिए गुणनफल (-100) और योग (0) है। टिप: विपरीत शून्यकों का योग (0) होता है।
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यदि परवलय के शून्यक (t-9) और (t+5) हैं, तो सममिति अक्ष कौन सा होगा?
If the zeroes of a parabola are (t-9) and (t+5), what will be its axis of symmetry?
#symbolic zeroes
#axis symmetry
#parabola
A (x=t-2)
B (x=t+2)
C (x=2t-4)
D (x=t-4)
Explanation opens after your attempt
Correct Answer
A. (x=t-2)
Step 1
Concept
The axis of symmetry is at the average of the zeroes, (\frac{(t-9)+(t+5)}{2}=t-2). Tip: take the midpoint even with symbols.
Step 2
Why this answer is correct
The correct answer is A. (x=t-2). The axis of symmetry is at the average of the zeroes, (\frac{(t-9)+(t+5)}{2}=t-2). Tip: take the midpoint even with symbols.
Step 3
Exam Tip
सममिति अक्ष शून्यकों के औसत पर है, (\frac{(t-9)+(t+5)}{2}=t-2)। टिप: प्रतीकों में भी मध्य मान लें।
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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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यदि ग्राफ (x=-15), (x=-5), (x=4) और (x=11) पर (x)-अक्ष को काटता है, तो शून्यकों की परास क्या है?
If a graph cuts the (x)-axis at (x=-15), (x=-5), (x=4), and (x=11), what is the range of the zeroes?
#range of zeroes
#number line
#graph
A (16)
B (20)
C (26)
D (-26)
Explanation opens after your attempt
Step 1
Concept
The range is the difference between the greatest and smallest zero, (11-(-15)=26). Tip: range is always non-negative.
Step 2
Why this answer is correct
The correct answer is C. (26). The range is the difference between the greatest and smallest zero, (11-(-15)=26). Tip: range is always non-negative.
Step 3
Exam Tip
परास सबसे बड़े और सबसे छोटे शून्यक का अंतर है, (11-(-15)=26)। टिप: परास हमेशा गैरऋणात्मक होती है।
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यदि (p(x)=(x+a)3 (x-b)2 ), जहाँ \(a\neq -b\), तो अलग शून्यक कौन से हैं?
If (p(x)=(x+a)3 (x-b)2 ), where \(a\neq -b\), what are the distinct zeroes?
#symbolic factors
#distinct zeroes
#multiplicity
A (-a) और (b) / (-a) and (b)
B (a) और (-b) / (a) and (-b)
C (-a), (b), (b)
D केवल (b) / Only (b)
Explanation opens after your attempt
Correct Answer
A. (-a) और (b) / (-a) and (b)
Step 1
Concept
From (x+a=0) we get (-a), and from (x-b=0) we get (b). Tip: do not count repetition among distinct zeroes.
Step 2
Why this answer is correct
The correct answer is A. (-a) और (b) / (-a) and (b). From (x+a=0) we get (-a), and from (x-b=0) we get (b). Tip: do not count repetition among distinct zeroes.
Step 3
Exam Tip
(x+a=0) से (-a) और (x-b=0) से (b) मिलता है। टिप: अलग शून्यकों में दोहराव न गिनें।
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यदि (p(x)=(x-1)2 (x+4)4 ) है, तो अलग वास्तविक शून्यकों की संख्या और ग्राफ का व्यवहार क्या है?
If (p(x)=(x-1)2 (x+4)4 ), what are the number of distinct real zeroes and graph behavior?
#even multiplicity
#distinct zeroes
#tangent
A दो, दोनों पर स्पर्श / Two, touches at both
B दो, दोनों पर कटान / Two, crosses at both
C छह, सभी पर स्पर्श / Six, touches at all
D एक, केवल (x=1) पर स्पर्श / One, touches only at (x=1)
Explanation opens after your attempt
Correct Answer
A. दो, दोनों पर स्पर्श / Two, touches at both
Step 1
Concept
There are two distinct zeroes (1) and (-4), and both have even powers. Tip: at an even-power zero the graph usually touches.
Step 2
Why this answer is correct
The correct answer is A. दो, दोनों पर स्पर्श / Two, touches at both. There are two distinct zeroes (1) and (-4), and both have even powers. Tip: at an even-power zero the graph usually touches.
Step 3
Exam Tip
दो अलग शून्यक (1) और (-4) हैं तथा दोनों की घात सम है। टिप: सम घात वाले शून्यक पर ग्राफ सामान्यतः स्पर्श करता है।
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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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यदि (p(-6)=0), (p(-2)<0), (p(5)=0), (p(9)>0) है, तो दिए गए शून्यकों के बीच दूरी क्या है?
If (p(-6)=0), (p(-2)<0), (p(5)=0), (p(9)>0), what is the distance between the given zeroes?
#function values
#distance
#zeroes
A (1)
B (11)
C (14)
D (-11)
Explanation opens after your attempt
Step 1
Concept
The given zeroes are (-6) and (5), so the distance is (5-(-6)=11). Tip: take only (x)-values where (p(x)=0).
Step 2
Why this answer is correct
The correct answer is B. (11). The given zeroes are (-6) and (5), so the distance is (5-(-6)=11). Tip: take only (x)-values where (p(x)=0).
Step 3
Exam Tip
दिए गए शून्यक (-6) और (5) हैं, इसलिए दूरी (5-(-6)=11) है। टिप: केवल (p(x)=0) वाले (x)-मान लें।
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एक ऊपर खुलने वाले परवलय के शून्यक (-4) और (10) हैं। (x=0) पर ग्राफ की स्थिति क्या होगी?
An upward-opening parabola has zeroes (-4) and (10). What will be the position of the graph at (x=0)?
#sign region
#upward parabola
#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
B. (x)-अक्ष के नीचे / Below the (x)-axis
Step 1
Concept
(0) lies between the two zeroes and an upward parabola stays below there. Tip: check the sign region between zeroes.
Step 2
Why this answer is correct
The correct answer is B. (x)-अक्ष के नीचे / Below the (x)-axis. (0) lies between the two zeroes and an upward parabola stays below there. Tip: check the sign region between zeroes.
Step 3
Exam Tip
(0) 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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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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यदि (p(x)=x-2 -2bx+b-2 -16) है तो ग्राफ के शून्यक कौन से होंगे?
If (p(x)=x-2 -2bx+b-2 -16), what will be the zeroes of the graph?
#symbolic quadratic
#difference of squares
#zeroes
A (b-4) और (b+4) / (b-4) and (b+4)
B (4-b) और (-b-4) / (4-b) and (-b-4)
C (b) और (16) / (b) and (16)
D कोई नहीं / None
Explanation opens after your attempt
Correct Answer
A. (b-4) और (b+4) / (b-4) and (b+4)
Step 1
Concept
It is ((x-b)2 -16), so \(x-b=\pm4\) and the zeroes are (b-4), (b+4). Tip: use difference of squares.
Step 2
Why this answer is correct
The correct answer is A. (b-4) और (b+4) / (b-4) and (b+4). It is ((x-b)2 -16), so \(x-b=\pm4\) and the zeroes are (b-4), (b+4). Tip: use difference of squares.
Step 3
Exam Tip
यह ((x-b)2 -16) है इसलिए \(x-b=\pm4\) और शून्यक (b-4), (b+4) हैं। टिप: वर्गों के अंतर का उपयोग करें।
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यदि ग्राफ (x)-अक्ष को ((-6,0)) और ((14,0)) 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 ((-6,0)) and ((14,0)), what change is needed to make the zeroes equally distant from the (y)-axis?
#symmetry
#y axis
#zeroes
A (14) को (6) करना होगा / (14) must be changed to (6)
B (-6) को (0) करना होगा / (-6) 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. (14) को (6) करना होगा / (14) must be changed to (6)
Step 1
Concept
For equal distance from the (y)-axis, zeroes should be opposites, so (6) is needed with (-6). Tip: symmetric zeroes are (a) and (-a).
Step 2
Why this answer is correct
The correct answer is A. (14) को (6) करना होगा / (14) must be changed to (6). For equal distance from the (y)-axis, zeroes should be opposites, so (6) is needed with (-6). Tip: symmetric zeroes are (a) and (-a).
Step 3
Exam Tip
(y)-अक्ष से समान दूरी के लिए शून्यक विपरीत होने चाहिए, इसलिए (-6) के साथ (6) चाहिए। टिप: सममित शून्यक (a) और (-a) होते हैं।
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यदि (p(-9)=0), (p(-4)=2), (p(2)=0), (p(6)=0) है तो कितने दिए गए (x)-मान शून्यक हैं?
If (p(-9)=0), (p(-4)=2), (p(2)=0), (p(6)=0), how many of the given (x)-values are zeroes?
#function table
#count zeroes
#graph
A दो / Two
B तीन / Three
C चार / Four
D एक / One
Explanation opens after your attempt
Correct Answer
B. तीन / Three
Step 1
Concept
The function value is (0) at (-9), (2), and (6). Tip: do not treat (p(-4)=2) as a zero.
Step 2
Why this answer is correct
The correct answer is B. तीन / Three. The function value is (0) at (-9), (2), and (6). Tip: do not treat (p(-4)=2) as a zero.
Step 3
Exam Tip
(-9), (2), (6) पर फलन मान (0) है। टिप: (p(-4)=2) को शून्यक न मानें।
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यदि (p(x)=x-2 -15x+56) है तो ग्राफ के शून्यकों के बीच दूरी कितनी है?
If (p(x)=x-2 -15x+56), what is the distance between the zeroes of the graph?
#distance between zeroes
#quadratic
#graph
A (1)
B (7)
C (15)
D (56)
Explanation opens after your attempt
Step 1
Concept
(x-2 -15x+56=(x-7)(x-8)), so the distance is (8-7=1). Tip: find zeroes first and then take distance.
Step 2
Why this answer is correct
The correct answer is A. (1). (x-2 -15x+56=(x-7)(x-8)), so the distance is (8-7=1). Tip: find zeroes first and then take distance.
Step 3
Exam Tip
(x-2 -15x+56=(x-7)(x-8)) है इसलिए दूरी (8-7=1) है। टिप: पहले शून्यक निकालें फिर दूरी लें।
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यदि ग्राफ (x)-अक्ष को ((7,0)) पर छूता है और ((-4,0)) पर काटता है तो शून्यकों का योग क्या है?
If a graph touches the (x)-axis at ((7,0)) and crosses it at ((-4,0)), what is the sum of the zeroes?
#sum of zeroes
#touching
#crossing
A (3)
B (11)
C (-11)
D (-3)
Explanation opens after your attempt
Step 1
Concept
The zeroes are (7) and (-4), so the sum is (3). Tip: count a touching point as a zero too.
Step 2
Why this answer is correct
The correct answer is A. (3). The zeroes are (7) and (-4), so the sum is (3). Tip: count a touching point as a zero too.
Step 3
Exam Tip
शून्यक (7) और (-4) हैं इसलिए योग (3) है। टिप: स्पर्श बिंदु को भी शून्यक मानें।
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यदि (p(x)=x-3 -8x-2 +15x) है तो ग्राफ के शून्यकों का समूह कौन सा है?
If (p(x)=x-3 -8x-2 +15x), what is the set of zeroes of the graph?
#cubic factorization
#zeroes
#graph
A (0,3,5)
B (0,-3,-5)
C (3,5,8)
D केवल (0) / Only (0)
Explanation opens after your attempt
Correct Answer
A. (0,3,5)
Step 1
Concept
(x-3 -8x-2 +15x=x(x-3)(x-5)), so the zeroes are (0,3,5). Tip: first take (x) as the common factor.
Step 2
Why this answer is correct
The correct answer is A. (0,3,5). (x-3 -8x-2 +15x=x(x-3)(x-5)), so the zeroes are (0,3,5). Tip: first take (x) as the common factor.
Step 3
Exam Tip
(x-3 -8x-2 +15x=x(x-3)(x-5)) है इसलिए शून्यक (0,3,5) हैं। टिप: पहले (x) सामान्य गुणनखंड निकालें।
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यदि (x)-अक्ष से मिलने वाले बिंदु ((-5,0)), ((-5,0)), ((4,0)) लिखे हैं तो अलग वास्तविक शून्यक कितने हैं?
If the points meeting the (x)-axis are written as ((-5,0)), ((-5,0)), ((4,0)), how many distinct real zeroes are there?
#repeated point
#distinct zeroes
#graph
A एक / One
B दो / Two
C तीन / Three
D चार / Four
Explanation opens after your attempt
Step 1
Concept
((-5,0)) is repeated, so the distinct zeroes are (-5) and (4). Tip: count the same (x)-value once.
Step 2
Why this answer is correct
The correct answer is B. दो / Two. ((-5,0)) is repeated, so the distinct zeroes are (-5) and (4). Tip: count the same (x)-value once.
Step 3
Exam Tip
((-5,0)) दोहराया गया है इसलिए अलग शून्यक (-5) और (4) हैं। टिप: समान (x)-मान को एक बार गिनें।
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यदि ग्राफ के शून्यक (-6), (2), (9) हैं तो (x)-अक्ष कटान बिंदुओं का सही समूह कौन सा है?
If the zeroes of a graph are (-6), (2), (9), which is the correct set of (x)-axis intersection points?
#zeroes to points
#graph
#coordinates
A ((0,-6)), ((0,2)), ((0,9))
B ((-6,0)), ((2,0)), ((9,0))
C ((-6,2)), ((2,9)), ((9,-6))
D ((6,0)), ((-2,0)), ((-9,0))
Explanation opens after your attempt
Correct Answer
B. ((-6,0)), ((2,0)), ((9,0))
Step 1
Concept
A zero (r) gives the point ((r,0)). Tip: write the zero as the first coordinate.
Step 2
Why this answer is correct
The correct answer is B. ((-6,0)), ((2,0)), ((9,0)). A zero (r) gives the point ((r,0)). Tip: write the zero as the first coordinate.
Step 3
Exam Tip
शून्यक (r) का बिंदु ((r,0)) होता है। टिप: शून्यक को पहले निर्देशांक में लिखें।
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यदि परवलय के शून्यक (c-7) और (c+3) हैं तो सममिति अक्ष कौन सा होगा?
If the zeroes of a parabola are (c-7) and (c+3), what will be its axis of symmetry?
#symbolic zeroes
#axis of symmetry
#parabola
A (x=c-2)
B (x=c+2)
C (x=2c-4)
D (x=c-4)
Explanation opens after your attempt
Correct Answer
A. (x=c-2)
Step 1
Concept
The axis of symmetry is at the average of the zeroes, (\frac{(c-7)+(c+3)}{2}=c-2). Tip: the average rule also works with symbols.
Step 2
Why this answer is correct
The correct answer is A. (x=c-2). The axis of symmetry is at the average of the zeroes, (\frac{(c-7)+(c+3)}{2}=c-2). Tip: the average rule also works with symbols.
Step 3
Exam Tip
सममिति अक्ष शून्यकों के औसत पर है (\frac{(c-7)+(c+3)}{2}=c-2)। टिप: प्रतीकों में भी औसत का नियम लागू होता है।
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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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यदि ग्राफ (x=-12), (x=-3), (x=8) पर (x)-अक्ष को काटता है तो शून्यकों की परास क्या है?
If a graph cuts the (x)-axis at (x=-12), (x=-3), (x=8), what is the range of the zeroes?
#range of zeroes
#number line
#graph
A (11)
B (15)
C (20)
D (-20)
Explanation opens after your attempt
Step 1
Concept
The range is the difference between the greatest and smallest zero, (8-(-12)=20). Tip: range is not negative.
Step 2
Why this answer is correct
The correct answer is C. (20). The range is the difference between the greatest and smallest zero, (8-(-12)=20). Tip: range is not negative.
Step 3
Exam Tip
परास सबसे बड़े और सबसे छोटे शून्यक का अंतर है (8-(-12)=20)। टिप: परास ऋणात्मक नहीं होती।
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यदि (p(x)=(x-4)(x+7)3 ) है तो अलग शून्यक कौन से हैं?
If (p(x)=(x-4)(x+7)3 ), what are the distinct zeroes?
#distinct zeroes
#repeated factor
#graph
A (4) और (-7) / (4) and (-7)
B (-4) और (7) / (-4) and (7)
C (4), (-7), (-7), (-7)
D केवल (-7) / Only (-7)
Explanation opens after your attempt
Correct Answer
A. (4) और (-7) / (4) and (-7)
Step 1
Concept
The zeroes are (4) and (-7), but (-7) is repeated. Tip: count repetition once for distinct zeroes.
Step 2
Why this answer is correct
The correct answer is A. (4) और (-7) / (4) and (-7). The zeroes are (4) and (-7), but (-7) is repeated. Tip: count repetition once for distinct zeroes.
Step 3
Exam Tip
शून्यक (4) और (-7) हैं पर (-7) दोहराया गया है। टिप: अलग शून्यक में दोहराव को एक बार गिनें।
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यदि (p(-8)=0), (p(-2)>0), (p(3)=0) और (p(9)<0) है तो दिए गए शून्यकों का योग क्या है?
If (p(-8)=0), (p(-2)>0), (p(3)=0) and (p(9)<0), what is the sum of the given zeroes?
#function values
#sum of zeroes
#graph
A (-5)
B (5)
C (-11)
D (0)
Explanation opens after your attempt
Step 1
Concept
The given zeroes are (-8) and (3), so their sum is (-5). Tip: take only the (x)-values where (p(x)=0).
Step 2
Why this answer is correct
The correct answer is A. (-5). The given zeroes are (-8) and (3), so their sum is (-5). Tip: take only the (x)-values where (p(x)=0).
Step 3
Exam Tip
दिए गए शून्यक (-8) और (3) हैं इसलिए योग (-5) है। टिप: केवल (p(x)=0) वाले (x)-मान लें।
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यदि परवलय के शून्यक (-7) और (5) हैं तथा वह ऊपर की ओर खुलता है तो (x=-1) पर ग्राफ कहाँ होगा?
If a parabola has zeroes (-7) and (5) and opens upward, where will the graph be at (x=-1)?
#sign region
#upward parabola
#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
B. (x)-अक्ष के नीचे / Below the (x)-axis
Step 1
Concept
(x=-1) lies between the zeroes and an upward-opening parabola is below the axis there. Tip: check the sign region between zeroes.
Step 2
Why this answer is correct
The correct answer is B. (x)-अक्ष के नीचे / Below the (x)-axis. (x=-1) lies between the zeroes and an upward-opening parabola is below the axis there. Tip: check the sign region between zeroes.
Step 3
Exam Tip
(x=-1) दोनों शून्यकों के बीच है और ऊपर खुलने वाले परवलय में बीच का भाग नीचे होता है। टिप: शून्यकों के बीच संकेत क्षेत्र देखें।
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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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यदि (p(x)=x-2 -2ax+a-2 -9) है, तो ग्राफ के शून्यक कौन से होंगे?
If (p(x)=x-2 -2ax+a-2 -9), what will be the zeroes of the graph?
#symbolic quadratic
#difference of squares
#zeroes
A (a-3) और (a+3) / (a-3) and (a+3)
B (3-a) और (-a-3) / (3-a) and (-a-3)
C (a) और (9) / (a) and (9)
D कोई नहीं / None
Explanation opens after your attempt
Correct Answer
A. (a-3) और (a+3) / (a-3) and (a+3)
Step 1
Concept
It is ((x-a)2 -9), so \(x-a=\pm3\) and the zeroes are (a-3), (a+3). Tip: use difference of squares.
Step 2
Why this answer is correct
The correct answer is A. (a-3) और (a+3) / (a-3) and (a+3). It is ((x-a)2 -9), so \(x-a=\pm3\) and the zeroes are (a-3), (a+3). Tip: use difference of squares.
Step 3
Exam Tip
यह ((x-a)2 -9) है, इसलिए \(x-a=\pm3\) और शून्यक (a-3), (a+3) हैं। टिप: वर्गों के अंतर का उपयोग करें।
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यदि ग्राफ (x)-अक्ष को ((-4,0)) और ((10,0)) 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 ((-4,0)) and ((10,0)), what change is needed to make the zeroes equally distant from the (y)-axis?
#symmetry
#y axis
#zeroes
A (10) को (4) करना होगा / (10) must be changed to (4)
B (-4) को (0) करना होगा / (-4) 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. (10) को (4) करना होगा / (10) must be changed to (4)
Step 1
Concept
For equal distance from the (y)-axis, zeroes should be opposites, so (4) is needed with (-4). Tip: symmetric zeroes are (a) and (-a).
Step 2
Why this answer is correct
The correct answer is A. (10) को (4) करना होगा / (10) must be changed to (4). For equal distance from the (y)-axis, zeroes should be opposites, so (4) is needed with (-4). Tip: symmetric zeroes are (a) and (-a).
Step 3
Exam Tip
(y)-अक्ष से समान दूरी के लिए शून्यक विपरीत होने चाहिए, इसलिए (-4) के साथ (4) चाहिए। टिप: सममित शून्यक (a) और (-a) होते हैं।
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यदि (p(-7)=0), (p(-3)=2), (p(1)=0), (p(4)=0), तो कितने दिए गए (x)-मान शून्यक हैं?
If (p(-7)=0), (p(-3)=2), (p(1)=0), (p(4)=0), how many of the given (x)-values are zeroes?
#function table
#count zeroes
#graph
A दो / Two
B तीन / Three
C चार / Four
D एक / One
Explanation opens after your attempt
Correct Answer
B. तीन / Three
Step 1
Concept
The function value is (0) at (-7), (1), and (4). Tip: do not treat (p(-3)=2) as a zero.
Step 2
Why this answer is correct
The correct answer is B. तीन / Three. The function value is (0) at (-7), (1), and (4). Tip: do not treat (p(-3)=2) as a zero.
Step 3
Exam Tip
(-7), (1), (4) पर फलन मान (0) है। टिप: (p(-3)=2) को शून्यक न मानें।
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यदि (p(x)=x-2 -13x+42) है, तो ग्राफ के शून्यकों के बीच दूरी कितनी है?
If (p(x)=x-2 -13x+42), what is the distance between the zeroes of the graph?
#distance between zeroes
#quadratic
#graph
A (1)
B (6)
C (13)
D (42)
Explanation opens after your attempt
Step 1
Concept
(x-2 -13x+42=(x-6)(x-7)), so the distance is (7-6=1). Tip: find zeroes first and then take distance.
Step 2
Why this answer is correct
The correct answer is A. (1). (x-2 -13x+42=(x-6)(x-7)), so the distance is (7-6=1). Tip: find zeroes first and then take distance.
Step 3
Exam Tip
(x-2 -13x+42=(x-6)(x-7)) है, इसलिए दूरी (7-6=1) है। टिप: पहले शून्यक निकालें फिर दूरी लें।
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यदि ग्राफ (x)-अक्ष को ((5,0)) पर छूता है और ((-3,0)) पर काटता है, तो शून्यकों का योग क्या है?
If a graph touches the (x)-axis at ((5,0)) and crosses it at ((-3,0)), what is the sum of the zeroes?
#sum of zeroes
#touching
#crossing
A (2)
B (8)
C (-8)
D (-2)
Explanation opens after your attempt
Step 1
Concept
The zeroes are (5) and (-3), so the sum is (2). Tip: count a touching point as a zero too.
Step 2
Why this answer is correct
The correct answer is A. (2). The zeroes are (5) and (-3), so the sum is (2). Tip: count a touching point as a zero too.
Step 3
Exam Tip
शून्यक (5) और (-3) हैं, इसलिए योग (2) है। टिप: स्पर्श बिंदु को भी शून्यक मानें।
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यदि (p(x)=x-3 -6x-2 +5x) है, तो ग्राफ के शून्यकों का समूह कौन सा है?
If (p(x)=x-3 -6x-2 +5x), what is the set of zeroes of the graph?
#cubic factorization
#zeroes
#graph
A (0,1,5)
B (0,-1,-5)
C (1,5,6)
D केवल (0) / Only (0)
Explanation opens after your attempt
Correct Answer
A. (0,1,5)
Step 1
Concept
(x-3 -6x-2 +5x=x(x-1)(x-5)), so the zeroes are (0,1,5). Tip: first take (x) as the common factor.
Step 2
Why this answer is correct
The correct answer is A. (0,1,5). (x-3 -6x-2 +5x=x(x-1)(x-5)), so the zeroes are (0,1,5). Tip: first take (x) as the common factor.
Step 3
Exam Tip
(x-3 -6x-2 +5x=x(x-1)(x-5)) है, इसलिए शून्यक (0,1,5) हैं। टिप: पहले (x) सामान्य गुणनखंड निकालें।
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यदि (x)-अक्ष से मिलने वाले बिंदु ((2,0)), ((2,0)), ((9,0)) लिखे हैं, तो अलग वास्तविक शून्यक कितने हैं?
If the points meeting the (x)-axis are written as ((2,0)), ((2,0)), ((9,0)), how many distinct real zeroes are there?
#repeated point
#distinct zeroes
#graph
A एक / One
B दो / Two
C तीन / Three
D चार / Four
Explanation opens after your attempt
Step 1
Concept
((2,0)) is repeated, so the distinct zeroes are (2) and (9). Tip: count the same (x)-value once.
Step 2
Why this answer is correct
The correct answer is B. दो / Two. ((2,0)) is repeated, so the distinct zeroes are (2) and (9). Tip: count the same (x)-value once.
Step 3
Exam Tip
((2,0)) दोहराया गया है, इसलिए अलग शून्यक (2) और (9) हैं। टिप: समान (x)-मान को एक बार गिनें।
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यदि ग्राफ के शून्यक (-4), (1), (8) हैं, तो (x)-अक्ष कटान बिंदुओं का सही समूह कौन सा है?
If the zeroes of a graph are (-4), (1), (8), which is the correct set of (x)-axis intersection points?
#zeroes to points
#graph
#coordinates
A ((0,-4)), ((0,1)), ((0,8))
B ((-4,0)), ((1,0)), ((8,0))
C ((-4,1)), ((1,8)), ((8,-4))
D ((4,0)), ((-1,0)), ((-8,0))
Explanation opens after your attempt
Correct Answer
B. ((-4,0)), ((1,0)), ((8,0))
Step 1
Concept
A zero (r) gives the point ((r,0)). Tip: write the zero as the first coordinate.
Step 2
Why this answer is correct
The correct answer is B. ((-4,0)), ((1,0)), ((8,0)). A zero (r) gives the point ((r,0)). Tip: write the zero as the first coordinate.
Step 3
Exam Tip
शून्यक (r) का बिंदु ((r,0)) होता है। टिप: शून्यक को पहले निर्देशांक में लिखें।
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यदि परवलय के शून्यक (b-5) और (b+1) हैं, तो सममिति अक्ष कौन सा होगा?
If the zeroes of a parabola are (b-5) and (b+1), what will be its axis of symmetry?
#symbolic zeroes
#axis of symmetry
#parabola
A (x=b-2)
B (x=b+2)
C (x=2b-4)
D (x=b-4)
Explanation opens after your attempt
Correct Answer
A. (x=b-2)
Step 1
Concept
The axis of symmetry is at the average of the zeroes, (\frac{(b-5)+(b+1)}{2}=b-2). Tip: the average rule also works with symbols.
Step 2
Why this answer is correct
The correct answer is A. (x=b-2). The axis of symmetry is at the average of the zeroes, (\frac{(b-5)+(b+1)}{2}=b-2). Tip: the average rule also works with symbols.
Step 3
Exam Tip
सममिति अक्ष शून्यकों के औसत पर है, (\frac{(b-5)+(b+1)}{2}=b-2)। टिप: प्रतीकों में भी औसत का नियम लागू होता है।
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यदि ग्राफ (x=-10), (x=-4), (x=6) पर (x)-अक्ष को काटता है, तो शून्यकों की परास क्या है?
If a graph cuts the (x)-axis at (x=-10), (x=-4), (x=6), what is the range of the zeroes?
#range of zeroes
#number line
#graph
A (10)
B (12)
C (16)
D (-16)
Explanation opens after your attempt
Step 1
Concept
The range is the difference between the greatest and smallest zero, (6-(-10)=16). Tip: range is not negative.
Step 2
Why this answer is correct
The correct answer is C. (16). The range is the difference between the greatest and smallest zero, (6-(-10)=16). Tip: range is not negative.
Step 3
Exam Tip
परास सबसे बड़े और सबसे छोटे शून्यक का अंतर है, (6-(-10)=16)। टिप: परास ऋणात्मक नहीं होती।
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यदि (p(x)=(x-2)(x+6)3 ) है, तो अलग शून्यक कौन से हैं?
If (p(x)=(x-2)(x+6)3 ), what are the distinct zeroes?
#distinct zeroes
#repeated factor
#graph
A (2) और (-6) / (2) and (-6)
B (-2) और (6) / (-2) and (6)
C (2), (-6), (-6), (-6)
D केवल (-6) / Only (-6)
Explanation opens after your attempt
Correct Answer
A. (2) और (-6) / (2) and (-6)
Step 1
Concept
The zeroes are (2) and (-6), but (-6) is repeated. Tip: count repetition once for distinct zeroes.
Step 2
Why this answer is correct
The correct answer is A. (2) और (-6) / (2) and (-6). The zeroes are (2) and (-6), but (-6) is repeated. Tip: count repetition once for distinct zeroes.
Step 3
Exam Tip
शून्यक (2) और (-6) हैं, पर (-6) दोहराया गया है। टिप: अलग शून्यक में दोहराव एक बार गिनें।
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यदि (p(-6)=0), (p(-1)>0), (p(4)=0) और (p(7)<0) है, तो दिए गए शून्यकों का गुणनफल क्या है?
If (p(-6)=0), (p(-1)>0), (p(4)=0) and (p(7)<0), what is the product of the given zeroes?
#function values
#product of zeroes
#graph
A (-24)
B (24)
C (-7)
D (0)
Explanation opens after your attempt
Step 1
Concept
The given zeroes are (-6) and (4), so the product is (-24). Tip: take only (x)-values where (p(x)=0).
Step 2
Why this answer is correct
The correct answer is A. (-24). The given zeroes are (-6) and (4), so the product is (-24). Tip: take only (x)-values where (p(x)=0).
Step 3
Exam Tip
दिए गए शून्यक (-6) और (4) हैं, इसलिए गुणनफल (-24) है। टिप: केवल (p(x)=0) वाले (x)-मान लें।
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यदि किसी परवलय के शून्यक (-8) और (2) हैं तथा वह ऊपर की ओर खुलता है, तो (x=-3) पर ग्राफ कहाँ होगा?
If a parabola has zeroes (-8) and (2) and opens upward, where will the graph be at (x=-3)?
#sign region
#upward parabola
#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
B. (x)-अक्ष के नीचे / Below the (x)-axis
Step 1
Concept
(x=-3) lies between the two zeroes, and an upward parabola is below the axis there. Tip: check the sign between zeroes.
Step 2
Why this answer is correct
The correct answer is B. (x)-अक्ष के नीचे / Below the (x)-axis. (x=-3) lies between the two zeroes, and an upward parabola is below the axis there. Tip: check the sign between zeroes.
Step 3
Exam Tip
(x=-3) दोनों शून्यकों के बीच है और ऊपर खुलने वाले परवलय में बीच का भाग नीचे होता है। टिप: शून्यकों के बीच संकेत देखें।
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यदि ग्राफ (x)-अक्ष को ((-3,0)) और ((9,0)) 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 ((-3,0)) and ((9,0)), what change is needed to make the zeroes equally distant from the (y)-axis?
#symmetry
#y axis
#zeroes
A (9) को (3) करना होगा / (9) must be changed to (3)
B (-3) को (0) करना होगा / (-3) must be changed to (0)
C दोनों को धनात्मक करना होगा / Both must be made positive
D कोई परिवर्तन नहीं चाहिए / No change is needed
Explanation opens after your attempt
Correct Answer
A. (9) को (3) करना होगा / (9) must be changed to (3)
Step 1
Concept
For equal distance from the (y)-axis, zeroes should be opposites, so (3) is needed with (-3). Tip: symmetric zeroes are (a) and (-a).
Step 2
Why this answer is correct
The correct answer is A. (9) को (3) करना होगा / (9) must be changed to (3). For equal distance from the (y)-axis, zeroes should be opposites, so (3) is needed with (-3). Tip: symmetric zeroes are (a) and (-a).
Step 3
Exam Tip
(y)-अक्ष से समान दूरी के लिए शून्यक विपरीत होने चाहिए, इसलिए (-3) के साथ (3) चाहिए। टिप: सममित शून्यक (a) और (-a) होते हैं।
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यदि किसी ग्राफ में (p(-4)=0), (p(0)=3), (p(2)=0), (p(5)=0), तो कितने दिए गए (x)-मान शून्यक हैं?
If in a graph (p(-4)=0), (p(0)=3), (p(2)=0), (p(5)=0), how many of the given (x)-values are zeroes?
#function table
#count zeroes
#graph
A दो / Two
B तीन / Three
C चार / Four
D एक / One
Explanation opens after your attempt
Correct Answer
B. तीन / Three
Step 1
Concept
The function value is (0) at (-4), (2), and (5). Tip: do not treat (p(0)=3) as a zero.
Step 2
Why this answer is correct
The correct answer is B. तीन / Three. The function value is (0) at (-4), (2), and (5). Tip: do not treat (p(0)=3) as a zero.
Step 3
Exam Tip
(-4), (2), (5) पर फलन मान (0) है। टिप: (p(0)=3) को शून्यक न मानें।
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यदि (p(x)=x-2 -11x+30) है, तो ग्राफ के शून्यकों के बीच दूरी कितनी है?
If (p(x)=x-2 -11x+30), what is the distance between the zeroes of the graph?
#distance between zeroes
#quadratic
#graph
A (1)
B (5)
C (11)
D (30)
Explanation opens after your attempt
Step 1
Concept
(x-2 -11x+30=(x-5)(x-6)), so the distance is (6-5=1). Tip: find zeroes first and then take the distance.
Step 2
Why this answer is correct
The correct answer is A. (1). (x-2 -11x+30=(x-5)(x-6)), so the distance is (6-5=1). Tip: find zeroes first and then take the distance.
Step 3
Exam Tip
(x-2 -11x+30=(x-5)(x-6)), इसलिए दूरी (6-5=1) है। टिप: पहले शून्यक निकालें फिर दूरी लें।
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यदि किसी ग्राफ का (x)-अक्ष से एक स्पर्श ((4,0)) पर है और एक कटान ((-2,0)) पर है, तो शून्यकों का योग क्या है?
If a graph touches the (x)-axis at ((4,0)) and crosses it at ((-2,0)), what is the sum of the zeroes?
#sum of zeroes
#touching
#crossing
A (2)
B (6)
C (-6)
D (-2)
Explanation opens after your attempt
Step 1
Concept
The zeroes are (4) and (-2), so the sum is (2). Tip: count a touching point as a zero too.
Step 2
Why this answer is correct
The correct answer is A. (2). The zeroes are (4) and (-2), so the sum is (2). Tip: count a touching point as a zero too.
Step 3
Exam Tip
शून्यक (4) और (-2) हैं, इसलिए योग (2) है। टिप: स्पर्श बिंदु को भी शून्यक मानें।
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यदि (p(x)=x-3 -4x-2 -5x) है, तो ग्राफ के शून्यकों का समूह कौन सा है?
If (p(x)=x-3 -4x-2 -5x), what is the set of zeroes of the graph?
#cubic factorization
#zeroes
#graph
A (0, -1, 5)
B (0, 1, -5)
C (4, -5, 0)
D केवल (0) / Only (0)
Explanation opens after your attempt
Correct Answer
A. (0, -1, 5)
Step 1
Concept
(x-3 -4x-2 -5x=x(x-5)(x+1)), so the zeroes are (0), (5), (-1). Tip: first take (x) as the common factor.
Step 2
Why this answer is correct
The correct answer is A. (0, -1, 5). (x-3 -4x-2 -5x=x(x-5)(x+1)), so the zeroes are (0), (5), (-1). Tip: first take (x) as the common factor.
Step 3
Exam Tip
(x-3 -4x-2 -5x=x(x-5)(x+1)), इसलिए शून्यक (0), (5), (-1) हैं। टिप: पहले (x) सामान्य गुणनखंड निकालें।
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यदि किसी ग्राफ पर शून्यक (-2), (3), (7) हैं, तो (x)-अक्ष कटान बिंदुओं का सही समूह कौन सा है?
If a graph has zeroes (-2), (3), (7), which is the correct set of (x)-axis intersection points?
#zeroes to points
#graph
#coordinates
A ((0,-2)), ((0,3)), ((0,7))
B ((-2,0)), ((3,0)), ((7,0))
C ((-2,3)), ((3,7)), ((7,-2))
D ((2,0)), ((-3,0)), ((-7,0))
Explanation opens after your attempt
Correct Answer
B. ((-2,0)), ((3,0)), ((7,0))
Step 1
Concept
A zero (a) gives the intersection point ((a,0)). Tip: write the zero as the first coordinate.
Step 2
Why this answer is correct
The correct answer is B. ((-2,0)), ((3,0)), ((7,0)). A zero (a) gives the intersection point ((a,0)). Tip: write the zero as the first coordinate.
Step 3
Exam Tip
शून्यक (a) का कटान बिंदु ((a,0)) होता है। टिप: शून्यक को पहले निर्देशांक में लिखें।
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यदि किसी परवलय के शून्यक (a-2) और (a+4) हैं, तो सममिति अक्ष कौन सा होगा?
If the zeroes of a parabola are (a-2) and (a+4), what will be its axis of symmetry?
#symbolic zeroes
#axis of symmetry
#parabola
A (x=a+1)
B (x=a+2)
C (x=2a+2)
D (x=a-1)
Explanation opens after your attempt
Correct Answer
A. (x=a+1)
Step 1
Concept
The axis of symmetry is at the average of zeroes, (\frac{(a-2)+(a+4)}{2}=a+1). Tip: take the average even for symbolic zeroes.
Step 2
Why this answer is correct
The correct answer is A. (x=a+1). The axis of symmetry is at the average of zeroes, (\frac{(a-2)+(a+4)}{2}=a+1). Tip: take the average even for symbolic zeroes.
Step 3
Exam Tip
सममिति अक्ष शून्यकों के औसत पर है, (\frac{(a-2)+(a+4)}{2}=a+1)। टिप: प्रतीकात्मक शून्यकों में भी औसत लें।
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यदि ग्राफ (x)-अक्ष को (x=-8), (x=-2), (x=4) पर काटता है, तो शून्यकों की परास क्या है?
If a graph cuts the (x)-axis at (x=-8), (x=-2), (x=4), what is the range of the zeroes?
#range of zeroes
#graph
#number line
A (6)
B (10)
C (12)
D (-12)
Explanation opens after your attempt
Step 1
Concept
The range is the difference between greatest and smallest zero, (4-(-8)=12). Tip: range is always non-negative.
Step 2
Why this answer is correct
The correct answer is C. (12). The range is the difference between greatest and smallest zero, (4-(-8)=12). Tip: range is always non-negative.
Step 3
Exam Tip
परास सबसे बड़े और सबसे छोटे शून्यक का अंतर है, (4-(-8)=12)। टिप: परास हमेशा गैरऋणात्मक होती है।
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यदि (p(x)=(x+1)(x-4)3 ) है, तो अलग शून्यक कौन से हैं?
If (p(x)=(x+1)(x-4)3 ), what are the distinct zeroes?
#distinct zeroes
#repeated factor
#graph
A (-1) और (4) / (-1) and (4)
B (1) और (-4) / (1) and (-4)
C (-1), (4), (4), (4)
D केवल (4) / Only (4)
Explanation opens after your attempt
Correct Answer
A. (-1) और (4) / (-1) and (4)
Step 1
Concept
The zeroes are (-1) and (4), but (4) is repeated. Tip: do not count repetition in distinct zeroes.
Step 2
Why this answer is correct
The correct answer is A. (-1) और (4) / (-1) and (4). The zeroes are (-1) and (4), but (4) is repeated. Tip: do not count repetition in distinct zeroes.
Step 3
Exam Tip
शून्यक (-1) और (4) हैं, पर (4) दोहराया गया है। टिप: अलग शून्यक में दोहराव न गिनें।
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यदि किसी ग्राफ पर (p(-5)>0), (p(-2)=0), (p(1)<0), (p(6)=0) है, तो दिए गए मानों में शून्यकों का योग क्या है?
If on a graph (p(-5)>0), (p(-2)=0), (p(1)<0), (p(6)=0), what is the sum of the zeroes among the given values?
#table values
#sum of zeroes
#graph
A (4)
B (-4)
C (7)
D (-1)
Explanation opens after your attempt
Step 1
Concept
The given zeroes are (-2) and (6), so the sum is (4). Tip: take only the (x)-values where (p(x)=0).
Step 2
Why this answer is correct
The correct answer is A. (4). The given zeroes are (-2) and (6), so the sum is (4). Tip: take only the (x)-values where (p(x)=0).
Step 3
Exam Tip
दिए गए शून्यक (-2) और (6) हैं, इसलिए योग (4) है। टिप: केवल (p(x)=0) वाले (x)-मान लें।
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यदि किसी बहुपद का ग्राफ (x)-अक्ष को ((-4,0)), ((2,0)), ((9,0)) पर काटता है, तो इन शून्यकों का गुणनफल क्या है?
If a polynomial graph cuts the (x)-axis at ((-4,0)), ((2,0)), ((9,0)), what is the product of these zeroes?
#product of zeroes
#coordinates
#graph
A (72)
B (-72)
C (7)
D (-11)
Explanation opens after your attempt
Step 1
Concept
The zeroes are (-4), (2), (9), and their product is (-72). Tip: multiply only the (x)-coordinates.
Step 2
Why this answer is correct
The correct answer is B. (-72). The zeroes are (-4), (2), (9), and their product is (-72). Tip: multiply only the (x)-coordinates.
Step 3
Exam Tip
शून्यक (-4), (2), (9) हैं और गुणनफल (-72) है। टिप: केवल (x)-निर्देशांकों को गुणा करें।
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किसी परवलय के शून्यक (-6) और (2) हैं। यदि वह ऊपर की ओर खुलता है, तो (x=-2) पर ग्राफ (x)-अक्ष के सापेक्ष कहाँ होगा?
The zeroes of a parabola are (-6) and (2). If it opens upward, where will the graph be relative to the (x)-axis at (x=-2)?
#parabola
#sign between zeroes
#graph
A (x)-अक्ष पर / On the (x)-axis
B (x)-अक्ष के ऊपर / Above the (x)-axis
C (x)-अक्ष के नीचे / Below the (x)-axis
D निर्धारित नहीं / Cannot be determined
Explanation opens after your attempt
Correct Answer
C. (x)-अक्ष के नीचे / Below the (x)-axis
Step 1
Concept
For an upward-opening parabola, the graph lies below the (x)-axis between the two zeroes. Tip: identify the sign region between zeroes.
Step 2
Why this answer is correct
The correct answer is C. (x)-अक्ष के नीचे / Below the (x)-axis. For an upward-opening parabola, the graph lies below the (x)-axis between the two zeroes. Tip: identify the sign region between zeroes.
Step 3
Exam Tip
ऊपर खुलने वाले परवलय में दो शून्यकों के बीच ग्राफ (x)-अक्ष के नीचे होता है। टिप: शून्यकों के बीच के क्षेत्र का संकेत पहचानें।
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यदि (p(x)=-(x-1)(x+4)) है तो ग्राफ के वास्तविक शून्यक कौन से हैं?
If (p(x)=-(x-1)(x+4)), what are the real zeroes of the graph?
#negative factor zeroes
A (1) और (-4) / (1) and (-4)
B (-1) और (4) / (-1) and (4)
C (0) और (-1) / (0) and (-1)
D कोई नहीं / None
Explanation opens after your attempt
Correct Answer
A. (1) और (-4) / (1) and (-4)
Step 1
Concept
The outside negative sign does not change the zeroes. Tip: solve (x-1=0) and (x+4=0).
Step 2
Why this answer is correct
The correct answer is A. (1) और (-4) / (1) and (-4). The outside negative sign does not change the zeroes. Tip: solve (x-1=0) and (x+4=0).
Step 3
Exam Tip
बाहरी ऋण चिह्न शून्यकों को नहीं बदलता। टिप: (x-1=0) और (x+4=0) हल करें।
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यदि ग्राफ (x)-अक्ष को ((2,0)) और ((14,0)) पर काटता है तो शून्यकों का औसत क्या है?
If a graph cuts the (x)-axis at ((2,0)) and ((14,0)), what is the average of the zeroes?
#average intercepts zeroes
A (6)
B (8)
C (12)
D (16)
Explanation opens after your attempt
Step 1
Concept
The average is \(\frac{2+14}{2}=8\). Tip: use the (x)-coordinates for the average.
Step 2
Why this answer is correct
The correct answer is B. (8). The average is \(\frac{2+14}{2}=8\). Tip: use the (x)-coordinates for the average.
Step 3
Exam Tip
औसत \(\frac{2+14}{2}=8\) है। टिप: औसत में (x)-निर्देशांकों का प्रयोग करें।
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यदि (p(x)=0) शून्य बहुपद है तो उसके शून्यकों के बारे में कौन सा कथन सही है?
If (p(x)=0) is the zero polynomial, which statement about its zeroes is correct?
#zero polynomial all zeroes
A केवल (0) शून्यक है / Only (0) is a zero
B हर वास्तविक (x) शून्यक है / Every real (x) is a zero
C कोई शून्यक नहीं है / There is no zero
D केवल धनात्मक (x) शून्यक हैं / Only positive (x) values are zeroes
Explanation opens after your attempt
Correct Answer
B. हर वास्तविक (x) शून्यक है / Every real (x) is a zero
Step 1
Concept
The zero polynomial gives (0) for every (x). Tip: treat it differently from a usual constant polynomial.
Step 2
Why this answer is correct
The correct answer is B. हर वास्तविक (x) शून्यक है / Every real (x) is a zero. The zero polynomial gives (0) for every (x). Tip: treat it differently from a usual constant polynomial.
Step 3
Exam Tip
शून्य बहुपद हर (x) पर (0) देता है। टिप: इसे सामान्य स्थिर बहुपद से अलग समझें।
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यदि ग्राफ (x)-अक्ष को ((-2,0)), ((3,0)), ((7,0)) पर काटता है तो शून्यकों का गुणनफल क्या है?
If a graph cuts the (x)-axis at ((-2,0)), ((3,0)), ((7,0)), what is the product of zeroes?
#product three zeroes
A (42)
B (-42)
C (8)
D (-12)
Explanation opens after your attempt
Step 1
Concept
The product is ((-2)\times3\times7=-42). Tip: multiply the (x)-values of all (x)-axis intersections.
Step 2
Why this answer is correct
The correct answer is B. (-42). The product is ((-2)\times3\times7=-42). Tip: multiply the (x)-values of all (x)-axis intersections.
Step 3
Exam Tip
गुणनफल ((-2)\times3\times7=-42) है। टिप: सभी (x)-अक्ष कटान के (x)-मानों को गुणा करें।
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यदि ग्राफ (x)-अक्ष को ((-5,0)) और ((5,0)) पर काटता है तो शून्यकों का गुणनफल क्या है?
If a graph cuts the (x)-axis at ((-5,0)) and ((5,0)), what is the product of zeroes?
#product opposite zeroes
A (0)
B (25)
C (-25)
D (10)
Explanation opens after your attempt
Step 1
Concept
The product is ((-5)\times5=-25). Tip: the product of opposite signs is negative.
Step 2
Why this answer is correct
The correct answer is C. (-25). The product is ((-5)\times5=-25). Tip: the product of opposite signs is negative.
Step 3
Exam Tip
गुणनफल ((-5)\times5=-25) है। टिप: विपरीत चिह्नों का गुणनफल ऋणात्मक होता है।
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एक ग्राफ (x)-अक्ष को ((a,0)), ((0,0)), ((-a,0)) पर काटता है जहाँ \(a\neq0\)। शून्यकों का योग क्या है?
A graph cuts the (x)-axis at ((a,0)), ((0,0)), ((-a,0)) where \(a\neq0\). What is the sum of zeroes?
#symbolic sum zeroes
A (a)
B (0)
C (2a)
D (-a)
Explanation opens after your attempt
Step 1
Concept
The zeroes are (a), (0), (-a), whose sum is (0). Tip: opposite numbers cancel each other.
Step 2
Why this answer is correct
The correct answer is B. (0). The zeroes are (a), (0), (-a), whose sum is (0). Tip: opposite numbers cancel each other.
Step 3
Exam Tip
शून्यक (a), (0), (-a) हैं जिनका योग (0) है। टिप: विपरीत संख्याएँ एक-दूसरे को काट देती हैं।
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यदि (p(x)=x-2 +x-6) है तो वास्तविक शून्यक कौन से हैं?
If (p(x)=x-2 +x-6), what are the real zeroes?
#quadratic zeroes factor
A (2) और (-3) / (2) and (-3)
B (-2) और (3) / (-2) and (3)
C (1) और (-6) / (1) and (-6)
D कोई नहीं / None
Explanation opens after your attempt
Correct Answer
A. (2) और (-3) / (2) and (-3)
Step 1
Concept
(x-2 +x-6=(x+3)(x-2)), so the zeroes are (-3) and (2). Tip: read the signs in the factors carefully.
Step 2
Why this answer is correct
The correct answer is A. (2) और (-3) / (2) and (-3). (x-2 +x-6=(x+3)(x-2)), so the zeroes are (-3) and (2). Tip: read the signs in the factors carefully.
Step 3
Exam Tip
(x-2 +x-6=(x+3)(x-2)) इसलिए शून्यक (-3) और (2) हैं। टिप: गुणनखंडों के चिह्न ध्यान से पढ़ें।
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यदि ग्राफ (x)-अक्ष को ((-3,0)), ((0,0)) और ((6,0)) पर काटता है तो शून्यकों का योग क्या है?
If a graph cuts the (x)-axis at ((-3,0)), ((0,0)) and ((6,0)), what is the sum of zeroes?
#sum zeroes origin
A (3)
B (6)
C (-3)
D (0)
Explanation opens after your attempt
Step 1
Concept
The sum is (-3+0+6=3). Tip: include the zero (0) from the origin.
Step 2
Why this answer is correct
The correct answer is A. (3). The sum is (-3+0+6=3). Tip: include the zero (0) from the origin.
Step 3
Exam Tip
योग (-3+0+6=3) है। टिप: मूल बिंदु का शून्यक (0) भी जोड़ें।
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