यदि (P) संख्या रेखा पर (4) से बाएँ \(\sqrt{9}\) इकाई है, तो (P) का मान क्या है?
If (P) is \(\sqrt{9}\) units left of (4) on the number line, what is the value of (P)?
#polynomials
#number-line
#direction
#perfect-square
A (1)
B (7)
C -(1)
D \(\sqrt{13}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{9}=3\), and moving left means subtracting, so (P=4-3=1). In direction questions, simplify the distance first.
Step 2
Why this answer is correct
The correct answer is A. (1). \(\sqrt{9}=3\), and moving left means subtracting, so (P=4-3=1). In direction questions, simplify the distance first.
Step 3
Exam Tip
\(\sqrt{9}=3\), और बाएँ जाने पर घटाते हैं, इसलिए (P=4-3=1)। दिशा वाले प्रश्न में पहले दूरी सरल करें।
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किस संख्या को संख्या रेखा पर \(\sqrt{25}-\sqrt{4}\) के रूप में दर्शाया जा सकता है?
Which number can be represented as \(\sqrt{25}-\sqrt{4}\) on the number line?
#polynomials
#number-line
#simplification
#perfect-square
A (3)
B (7)
C (21)
D \(\sqrt{21}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{25}=5\) and \(\sqrt{4}=2\), so \(\sqrt{25}-\sqrt{4}=3\). Simplify perfect squares immediately.
Step 2
Why this answer is correct
The correct answer is A. (3). \(\sqrt{25}=5\) and \(\sqrt{4}=2\), so \(\sqrt{25}-\sqrt{4}=3\). Simplify perfect squares immediately.
Step 3
Exam Tip
\(\sqrt{25}=5\) और \(\sqrt{4}=2\), इसलिए \(\sqrt{25}-\sqrt{4}=3\)। पूर्ण वर्गों को तुरंत सरल करें।
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संख्या रेखा पर \(\frac{\sqrt{16}}{2}\) किस बिंदु के बराबर है?
On the number line, \(\frac{\sqrt{16}}{2}\) is equal to which point?
#polynomials
#number-line
#simplification
#perfect-square
A (2)
B (4)
C (8)
D \(\frac{1}{2}\)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{16}=4\) and \(\frac{4}{2}=2\), so the point is (2). Simplify the square root first, then divide.
Step 2
Why this answer is correct
The correct answer is A. (2). \(\sqrt{16}=4\) and \(\frac{4}{2}=2\), so the point is (2). Simplify the square root first, then divide.
Step 3
Exam Tip
\(\sqrt{16}=4\) और \(\frac{4}{2}=2\), इसलिए बिंदु (2) है। पहले वर्गमूल सरल करें, फिर भाग दें।
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संख्या रेखा पर \(\sqrt{0.49}\) का सही स्थान कौन सा है?
What is the correct position of \(\sqrt{0.49}\) on the number line?
#number-line
#decimal-square-root
#perfect-square
#position
A (0.07)
B (0.7)
C (4.9)
D (7)
Explanation opens after your attempt
Step 1
Concept
Since \(0.7^2=0.49\), \(\sqrt{0.49}=0.7\). Be careful with place value in decimal squares.
Step 2
Why this answer is correct
The correct answer is B. (0.7). Since \(0.7^2=0.49\), \(\sqrt{0.49}=0.7\). Be careful with place value in decimal squares.
Step 3
Exam Tip
\(0.7^2=0.49\), इसलिए \(\sqrt{0.49}=0.7\) है। दशमलव वर्गों में स्थान मान सावधानी से देखें।
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संख्या रेखा पर \(\sqrt{25}\) और \(-\sqrt{9}\) के बीच की दूरी कितनी है?
What is the distance between \(\sqrt{25}\) and \(-\sqrt{9}\) on the number line?
#number-line
#distance
#perfect-square
#roots
A (2)
B (5)
C (8)
D (14)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{25}=5\) and \(-\sqrt{9}=-3\), so the distance is (|5-(-3)|=8). Simplify square roots first.
Step 2
Why this answer is correct
The correct answer is C. (8). \(\sqrt{25}=5\) and \(-\sqrt{9}=-3\), so the distance is (|5-(-3)|=8). Simplify square roots first.
Step 3
Exam Tip
\(\sqrt{25}=5\) और \(-\sqrt{9}=-3\), इसलिए दूरी (|5-(-3)|=8) है। पहले वर्गमूल सरल करें।
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कौन सा कथन संख्या रेखा पर \(-\sqrt{4}\) की सही स्थिति बताता है?
Which statement gives the correct position of \(-\sqrt{4}\) on the number line?
#number-line
#negative-root
#perfect-square
#medium
A यह (2) पर होगा / It will be at (2)
B यह (-2) पर होगा / It will be at (-2)
C यह (4) पर होगा / It will be at (4)
D यह (-4) पर होगा / It will be at (-4)
Explanation opens after your attempt
Correct Answer
B. यह (-2) पर होगा / It will be at (-2)
Step 1
Concept
\(\sqrt{4}=2\), so \(-\sqrt{4}=-2\). Remember the negative sign after finding the square root.
Step 2
Why this answer is correct
The correct answer is B. यह (-2) पर होगा / It will be at (-2). \(\sqrt{4}=2\), so \(-\sqrt{4}=-2\). Remember the negative sign after finding the square root.
Step 3
Exam Tip
\(\sqrt{4}=2\), इसलिए \(-\sqrt{4}=-2\) होगा। ऋण चिह्न को वर्गमूल लेने के बाद भी याद रखें।
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संख्या रेखा पर \(\sqrt{9}\) किस बिंदु के समान है?
On the number line \(\sqrt{9}\) is the same as which point?
#number-line
#square-root
#perfect-square
#easy
A (2)
B (3)
C (4)
D (9)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{9}=3\), so it is located at point (3). Learn square roots of perfect squares for quick answers.
Step 2
Why this answer is correct
The correct answer is B. (3). \(\sqrt{9}=3\), so it is located at point (3). Learn square roots of perfect squares for quick answers.
Step 3
Exam Tip
\(\sqrt{9}=3\), इसलिए यह बिंदु (3) पर होगा। पूर्ण वर्गों के वर्गमूल तुरंत पहचानें।
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संख्या रेखा पर \(\sqrt{16}\) का स्थान कौन-सा है?
What is the position of \(\sqrt{16}\) on the number line?
#perfect-square
#number-line
#square-root
A (4)
B (8)
C (16)
D -(4)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{16}=4\), so its position is (4). Square roots of perfect squares can be identified directly.
Step 2
Why this answer is correct
The correct answer is A. (4). \(\sqrt{16}=4\), so its position is (4). Square roots of perfect squares can be identified directly.
Step 3
Exam Tip
\(\sqrt{16}=4\), इसलिए इसका स्थान (4) है। पूर्ण वर्गों के वर्गमूल सीधे पहचाने जा सकते हैं।
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संख्या रेखा पर \(\sqrt{9}\) किस संख्या के बराबर है?
Which number is equal to \(\sqrt{9}\) on the number line?
#perfect-square
#square-root
#number-line
A (3)
B (9)
C \(\frac{1}{3}\)
D -(3)
Explanation opens after your attempt
Step 1
Concept
\(\sqrt{9}=3\), so it is at the point (3). The principal square root is taken positive.
Step 2
Why this answer is correct
The correct answer is A. (3). \(\sqrt{9}=3\), so it is at the point (3). The principal square root is taken positive.
Step 3
Exam Tip
\(\sqrt{9}=3\), इसलिए यह (3) के बिंदु पर होगा। वर्गमूल का मुख्य मान धनात्मक लिया जाता है।
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यदि (p(x)=x-2 -8x+16) है, तो (p(4+t)) का मान क्या है?
If (p(x)=x-2 -8x+16), what is the value of (p(4+t))?
#substitution
#perfect-square
#polynomial
A \(t^2\)
B \(t^2+4\)
C (4t)
D \(t^2-16\)
Explanation opens after your attempt
Correct Answer
A. \(t^2\)
Step 1
Concept
(p(x)=(x-4)2 ), so (p(4+t)=t-2 ). In such questions, first form a perfect square.
Step 2
Why this answer is correct
The correct answer is A. \(t^2\). (p(x)=(x-4)2 ), so (p(4+t)=t-2 ). In such questions, first form a perfect square.
Step 3
Exam Tip
(p(x)=(x-4)2 ), इसलिए (p(4+t)=t-2 )। ऐसे प्रश्नों में पहले पूर्ण वर्ग बनाना आसान होता है।
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यदि (p(x)=4x-2 -4x+1), तो इसके शून्यक क्या हैं?
If (p(x)=4x-2 -4x+1), what are its zeroes?
#equal-zeroes
#perfect-square
#quadratic
A \(\frac{1}{2},\frac{1}{2}\)
B (1,1)
C -\(\frac{1}{2},-\frac{1}{2}\)
D (2,2)
Explanation opens after your attempt
Correct Answer
A. \(\frac{1}{2},\frac{1}{2}\)
Step 1
Concept
(4x-2 -4x+1=(2x-1)2 ), so the zero \(\frac{1}{2}\) occurs twice. Perfect square form gives equal zeroes directly.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{1}{2},\frac{1}{2}\). (4x-2 -4x+1=(2x-1)2 ), so the zero \(\frac{1}{2}\) occurs twice. Perfect square form gives equal zeroes directly.
Step 3
Exam Tip
(4x-2 -4x+1=(2x-1)2 ), इसलिए शून्यक \(\frac{1}{2}\) दो बार है। पूर्ण वर्ग रूप तुरंत समान शून्यक देता है।
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यदि (p(x)=x-2 +kx+25) पूर्ण वर्ग बहुपद है और (k<0), तो (k) क्या है?
If (p(x)=x-2 +kx+25) is a perfect square polynomial and (k<0), what is (k)?
#perfect square
#parameter
#quadratic
A (-10)
B (-5)
C (5)
D (10)
Explanation opens after your attempt
Step 1
Concept
For (x-2 +kx+25=(x-5)2 ), (k=-10). In a perfect square, the middle term is (2ab).
Step 2
Why this answer is correct
The correct answer is A. (-10). For (x-2 +kx+25=(x-5)2 ), (k=-10). In a perfect square, the middle term is (2ab).
Step 3
Exam Tip
(x-2 +kx+25=(x-5)2 ) होने पर (k=-10)। पूर्ण वर्ग में मध्य पद (2ab) होता है।
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यदि (p(x)=x-4 +mx-2 +16) को (\(x^2-4\)2 ) के रूप में लिखा जा सकता है, तो (m) क्या है?
If (p(x)=x-4 +mx-2 +16) can be written as (\(x^2-4\)2 ), what is (m)?
#perfect square
#quartic
#identity
A (-8)
B (-4)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
(\(x^2-4\)2 =x-4 -8x-2 +16), so (m=-8). In a square identity, find the middle term (2ab) carefully.
Step 2
Why this answer is correct
The correct answer is A. (-8). (\(x^2-4\)2 =x-4 -8x-2 +16), so (m=-8). In a square identity, find the middle term (2ab) carefully.
Step 3
Exam Tip
(\(x^2-4\)2 =x-4 -8x-2 +16), इसलिए (m=-8)। वर्ग पहचान में मध्य पद (2ab) को ध्यान से निकालें।
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यदि (p(x)=4x-2 -12x+9), तो इसके शून्यकों का स्वरूप क्या है?
If (p(x)=4x-2 -12x+9), what is the nature of its zeroes?
#perfect-square
#equal-zeroes
#quadratic
A समान वास्तविक शून्यक \(\frac{3}{2},\frac{3}{2}\) / Equal real zeroes \(\frac{3}{2},\frac{3}{2}\)
B भिन्न वास्तविक शून्यक (3,2) / Distinct real zeroes (3,2)
C कोई वास्तविक शून्यक नहीं / No real zeroes
D एक शून्यक \(-\frac{3}{2}\) / One zero \(-\frac{3}{2}\)
Explanation opens after your attempt
Correct Answer
A. समान वास्तविक शून्यक \(\frac{3}{2},\frac{3}{2}\) / Equal real zeroes \(\frac{3}{2},\frac{3}{2}\)
Step 1
Concept
(4x-2 -12x+9=(2x-3)2 ), so the equal zeroes are \(\frac{3}{2}\). A perfect square form indicates equal zeroes.
Step 2
Why this answer is correct
The correct answer is A. समान वास्तविक शून्यक \(\frac{3}{2},\frac{3}{2}\) / Equal real zeroes \(\frac{3}{2},\frac{3}{2}\). (4x-2 -12x+9=(2x-3)2 ), so the equal zeroes are \(\frac{3}{2}\). A perfect square form indicates equal zeroes.
Step 3
Exam Tip
(4x-2 -12x+9=(2x-3)2 ), इसलिए समान शून्यक \(\frac{3}{2}\) हैं। पूर्ण वर्ग रूप समान शून्यक बताता है।
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यदि (p(x)=x-2 +6x+9) है, तो इसका शून्यक कैसा है?
If (p(x)=x-2 +6x+9), what type of zero does it have?
#equal-zeroes
#perfect-square
#polynomial
A दो समान शून्यक (-3,-3) / Two equal zeroes (-3,-3)
B दो भिन्न शून्यक (3,-3) / Two distinct zeroes (3,-3)
C कोई वास्तविक शून्यक नहीं / No real zero
D एक शून्यक (0) / One zero (0)
Explanation opens after your attempt
Correct Answer
A. दो समान शून्यक (-3,-3) / Two equal zeroes (-3,-3)
Step 1
Concept
(x-2 +6x+9=(x+3)2 ), so (-3) occurs twice. A perfect square trinomial gives equal zeroes.
Step 2
Why this answer is correct
The correct answer is A. दो समान शून्यक (-3,-3) / Two equal zeroes (-3,-3). (x-2 +6x+9=(x+3)2 ), so (-3) occurs twice. A perfect square trinomial gives equal zeroes.
Step 3
Exam Tip
(x-2 +6x+9=(x+3)2 ), इसलिए शून्यक (-3) दो बार आता है। पूर्ण वर्ग त्रिपद समान शून्यक देता है।
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यदि (p(x)=x-2 +kx+16) पूर्ण वर्ग बहुपद है और (k<0), तो (k) क्या है?
If (p(x)=x-2 +kx+16) is a perfect square polynomial and (k<0), what is (k)?
#perfect square
#parameter
#quadratic
A (-8)
B (-4)
C (4)
D (8)
Explanation opens after your attempt
Step 1
Concept
For (x-2 +kx+16=(x-4)2 ), (k=-8). In a perfect square, the middle term is (2ab).
Step 2
Why this answer is correct
The correct answer is A. (-8). For (x-2 +kx+16=(x-4)2 ), (k=-8). In a perfect square, the middle term is (2ab).
Step 3
Exam Tip
(x-2 +kx+16=(x-4)2 ) होने पर (k=-8)। पूर्ण वर्ग में मध्य पद (2ab) होता है।
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यदि (p(x)=4x-2 -12x+9), तो इसके शून्यकों के बारे में कौन सा कथन सही है?
If (p(x)=4x-2 -12x+9), which statement about its zeroes is correct?
#polynomials
#perfect_square
#zeroes
#hard
A दोनों शून्यक \(\frac{3}{2}\) हैं / Both zeroes are \(\frac{3}{2}\)
B दोनों शून्यक \(-\frac{3}{2}\) हैं / Both zeroes are \(-\frac{3}{2}\)
C शून्यक \(\frac{2}{3}\) और \(\frac{3}{2}\) हैं / Zeroes are \(\frac{2}{3}\) and \(\frac{3}{2}\)
D कोई शून्यक नहीं है / There is no zero
Explanation opens after your attempt
Correct Answer
A. दोनों शून्यक \(\frac{3}{2}\) हैं / Both zeroes are \(\frac{3}{2}\)
Step 1
Concept
(4x-2 -12x+9=(2x-3)2 ). Therefore, both zeroes are \(\frac{3}{2}\).
Step 2
Why this answer is correct
The correct answer is A. दोनों शून्यक \(\frac{3}{2}\) हैं / Both zeroes are \(\frac{3}{2}\). (4x-2 -12x+9=(2x-3)2 ). Therefore, both zeroes are \(\frac{3}{2}\).
Step 3
Exam Tip
(4x-2 -12x+9=(2x-3)2 ) है। इसलिए दोनों शून्यक \(\frac{3}{2}\) हैं।
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कौन सा बहुपद पूर्ण वर्ग है?
Which polynomial is a perfect square?
#perfect square
#identity
#polynomial
A \(x^2+10x+25\)
B \(x^2+10x+20\)
C \(x^2+5x+25\)
D \(x^2-10x-25\)
Explanation opens after your attempt
Correct Answer
A. \(x^2+10x+25\)
Step 1
Concept
(x-2 +10x+25=(x+5)2 ). Check the squares of first and last terms and the middle term (2ab).
Step 2
Why this answer is correct
The correct answer is A. \(x^2+10x+25\). (x-2 +10x+25=(x+5)2 ). Check the squares of first and last terms and the middle term (2ab).
Step 3
Exam Tip
(x-2 +10x+25=(x+5)2 ) है। पहले और अंतिम पद के वर्ग तथा मध्य पद (2ab) को जांचें।
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यदि (p(x)=x-2 +kx+9) पूर्ण वर्ग बहुपद है और (k>0), तो (k) क्या है?
If (p(x)=x-2 +kx+9) is a perfect square polynomial and (k>0), what is (k)?
#perfect square
#parameter
#quadratic
A (3)
B (6)
C (9)
D (18)
Explanation opens after your attempt
Step 1
Concept
For (x-2 +kx+9=(x+3)2 ), (k=6). In a perfect square, the middle term is (2ab).
Step 2
Why this answer is correct
The correct answer is B. (6). For (x-2 +kx+9=(x+3)2 ), (k=6). In a perfect square, the middle term is (2ab).
Step 3
Exam Tip
(x-2 +kx+9=(x+3)2 ) होने पर (k=6)। पूर्ण वर्ग में मध्य पद (2ab) होता है।
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(p(x)=x-2 +4x+4) के लिए निम्न में से कौन सा सत्य है?
Which of the following is true for (p(x)=x-2 +4x+4)?
#zero-of-polynomial
#perfect-square
#substitution
A (p(-2)=0)
B (p(0)=0)
C (p(2)=0)
D (p(4)=0)
Explanation opens after your attempt
Correct Answer
A. (p(-2)=0)
Step 1
Concept
(p(-2)=4-8+4=0). Therefore (-2) is a zero of this polynomial.
Step 2
Why this answer is correct
The correct answer is A. (p(-2)=0). (p(-2)=4-8+4=0). Therefore (-2) is a zero of this polynomial.
Step 3
Exam Tip
(p(-2)=4-8+4=0) है। इसलिए (-2) इस बहुपद का शून्य है।
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यदि \(z=5-2\sqrt{6}\), तो (z) को किस वर्ग के रूप में लिखा जा सकता है?
If \(z=5-2\sqrt{6}\), then (z) can be written as which square?
#surds
#perfect_square
#identity
A \((\sqrt{3}-\sqrt{2})^{2}\)
B \((\sqrt{6}-1)^{2}\)
C \((3-\sqrt{2})^{2}\)
D \((2-\sqrt{3})^{2}\)
Explanation opens after your attempt
Correct Answer
A. \((\sqrt{3}-\sqrt{2})^{2}\)
Step 1
Concept
(\(\sqrt{3}-\sqrt{2}\)^{2}=3+2-2\sqrt{6}=5-2\sqrt{6}). In exams, identify (a,b) from (a+b) and \(2\sqrt{ab}\).
Step 2
Why this answer is correct
The correct answer is A. \((\sqrt{3}-\sqrt{2})^{2}\). (\(\sqrt{3}-\sqrt{2}\)^{2}=3+2-2\sqrt{6}=5-2\sqrt{6}). In exams, identify (a,b) from (a+b) and \(2\sqrt{ab}\).
Step 3
Exam Tip
(\(\sqrt{3}-\sqrt{2}\)^{2}=3+2-2\sqrt{6}=5-2\sqrt{6})। परीक्षा में (a+b) और \(2\sqrt{ab}\) से (a,b) पहचानें।
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\(x^2-24x+144\) किसके बराबर है?
What is \(x^2-24x+144\) equal to?
#polynomials
#perfect square
#factorization
A ((x-12)2 )
B ((x+12)2 )
C ((x-24)2 )
D \(x^2-144\)
Explanation opens after your attempt
Correct Answer
A. ((x-12)2 )
Step 1
Concept
This is of the form \(x^2-2\cdot x\cdot12+12^2\). Hence ((x-12)2 ) is correct.
Step 2
Why this answer is correct
The correct answer is A. ((x-12)2 ). This is of the form \(x^2-2\cdot x\cdot12+12^2\). Hence ((x-12)2 ) is correct.
Step 3
Exam Tip
यह \(x^2-2\cdot x\cdot12+12^2\) का रूप है। इसलिए ((x-12)2 ) सही है।
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\(x^2+22x+121\) किसके बराबर है?
What is \(x^2+22x+121\) equal to?
#polynomials
#perfect square
#identity
A ((x+11)2 )
B ((x-11)2 )
C ((x+22)2 )
D \(x^2+121\)
Explanation opens after your attempt
Correct Answer
A. ((x+11)2 )
Step 1
Concept
This is \(x^2+2\cdot x\cdot11+11^2\). Therefore it is ((x+11)2 ).
Step 2
Why this answer is correct
The correct answer is A. ((x+11)2 ). This is \(x^2+2\cdot x\cdot11+11^2\). Therefore it is ((x+11)2 ).
Step 3
Exam Tip
यह \(x^2+2\cdot x\cdot11+11^2\) है। इसलिए यह ((x+11)2 ) है।
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\(x^2-20x+100\) किसके बराबर है?
What is \(x^2-20x+100\) equal to?
#polynomials
#perfect square
#factorization
A ((x-10)2 )
B ((x+10)2 )
C ((x-20)2 )
D \(x^2-100\)
Explanation opens after your attempt
Correct Answer
A. ((x-10)2 )
Step 1
Concept
This is \(x^2-2\cdot x\cdot10+10^2\). Hence ((x-10)2 ) is correct.
Step 2
Why this answer is correct
The correct answer is A. ((x-10)2 ). This is \(x^2-2\cdot x\cdot10+10^2\). Hence ((x-10)2 ) is correct.
Step 3
Exam Tip
यह \(x^2-2\cdot x\cdot10+10^2\) है। इसलिए ((x-10)2 ) सही है।
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\(x^2+18x+81\) किसके बराबर है?
What is \(x^2+18x+81\) equal to?
#polynomials
#perfect square
#identity
A ((x+9)2 )
B ((x-9)2 )
C ((x+18)2 )
D \(x^2+81\)
Explanation opens after your attempt
Correct Answer
A. ((x+9)2 )
Step 1
Concept
This is \(x^2+2\cdot x\cdot9+9^2\). Therefore it is ((x+9)2 ).
Step 2
Why this answer is correct
The correct answer is A. ((x+9)2 ). This is \(x^2+2\cdot x\cdot9+9^2\). Therefore it is ((x+9)2 ).
Step 3
Exam Tip
यह \(x^2+2\cdot x\cdot9+9^2\) है। इसलिए यह ((x+9)2 ) है।
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\(x^2-16x+64\) किसके बराबर है?
What is \(x^2-16x+64\) equal to?
#polynomials
#perfect square
#factorization
A ((x-8)2 )
B ((x+8)2 )
C ((x-16)2 )
D \(x^2-64\)
Explanation opens after your attempt
Correct Answer
A. ((x-8)2 )
Step 1
Concept
This is of the form \(x^2-2\cdot x\cdot8+8^2\). Hence ((x-8)2 ) is correct.
Step 2
Why this answer is correct
The correct answer is A. ((x-8)2 ). This is of the form \(x^2-2\cdot x\cdot8+8^2\). Hence ((x-8)2 ) is correct.
Step 3
Exam Tip
यह \(x^2-2\cdot x\cdot8+8^2\) का रूप है। इसलिए ((x-8)2 ) सही है।
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\(x^2+14x+49\) किसके बराबर है?
What is \(x^2+14x+49\) equal to?
#polynomials
#perfect square
#identity
A ((x+7)2 )
B ((x-7)2 )
C ((x+14)2 )
D \(x^2+49\)
Explanation opens after your attempt
Correct Answer
A. ((x+7)2 )
Step 1
Concept
This is \(x^2+2\cdot x\cdot7+7^2\). Therefore it is ((x+7)2 ).
Step 2
Why this answer is correct
The correct answer is A. ((x+7)2 ). This is \(x^2+2\cdot x\cdot7+7^2\). Therefore it is ((x+7)2 ).
Step 3
Exam Tip
यह \(x^2+2\cdot x\cdot7+7^2\) है। इसलिए यह ((x+7)2 ) है।
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यदि \(9x^2+12x+4=0\), तो मूलों की प्रकृति के बारे में सही कथन कौन सा है?
If \(9x^2+12x+4=0\), which statement about the nature of roots is correct?
#quadratic_equations
#nature_of_roots
#perfect_square
A मूल वास्तविक और बराबर हैं / Roots are real and equal
B मूल वास्तविक और भिन्न हैं / Roots are real and distinct
C मूल वास्तविक नहीं हैं / Roots are not real
D मूल अपरिमेय हैं / Roots are irrational
Explanation opens after your attempt
Correct Answer
A. मूल वास्तविक और बराबर हैं / Roots are real and equal
Step 1
Concept
Here \(D=12^2-4\cdot9\cdot4=0\), so the roots are real and equal. In exams, \(9x^2+12x+4\) can also be recognized as ((3x+2)2 ).
Step 2
Why this answer is correct
The correct answer is A. मूल वास्तविक और बराबर हैं / Roots are real and equal. Here \(D=12^2-4\cdot9\cdot4=0\), so the roots are real and equal. In exams, \(9x^2+12x+4\) can also be recognized as ((3x+2)2 ).
Step 3
Exam Tip
यहां \(D=12^2-4\cdot9\cdot4=0\), इसलिए मूल वास्तविक और बराबर हैं। परीक्षा में \(9x^2+12x+4\) को ((3x+2)2 ) भी पहचान सकते हैं।
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समीकरण \(12x^2-12x+3=0\) में मूलों की प्रकृति क्या है?
What is the nature of roots in \(12x^2-12x+3=0\)?
#quadratic-equations
#equal-roots
#perfect-square
A दो वास्तविक और समान ((D=0)) / Two real and equal ((D=0))
B दो वास्तविक और असमान ((D=12)) / Two real and distinct ((D=12))
C कोई वास्तविक मूल नहीं ((D<0)) / No real roots ((D<0))
D दो परिमेय असमान ((D=144)) / Two rational distinct roots ((D=144))
Explanation opens after your attempt
Correct Answer
A. दो वास्तविक और समान ((D=0)) / Two real and equal ((D=0))
Step 1
Concept
Here (D=(-12)2 -4(12)(3)=0). It can also be written as (3(2x-1)2 =0).
Step 2
Why this answer is correct
The correct answer is A. दो वास्तविक और समान ((D=0)) / Two real and equal ((D=0)). Here (D=(-12)2 -4(12)(3)=0). It can also be written as (3(2x-1)2 =0).
Step 3
Exam Tip
यहाँ (D=(-12)2 -4(12)(3)=0) है। इसे (3(2x-1)2 =0) भी लिख सकते हैं।
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समीकरण \(16x^2+24x+9=0\) के लिए सही कथन चुनिए।
Choose the correct statement for \(16x^2+24x+9=0\).
#quadratic-equations
#equal-root-value
#perfect-square
A मूल समान हैं और \(x=-\frac{3}{4}\) / Roots are equal and \(x=-\frac{3}{4}\)
B मूल समान हैं और \(x=\frac{3}{4}\) / Roots are equal and \(x=\frac{3}{4}\)
C मूल असमान हैं और (D=9) / Roots are distinct and (D=9)
D कोई वास्तविक मूल नहीं हैं / There are no real roots
Explanation opens after your attempt
Correct Answer
A. मूल समान हैं और \(x=-\frac{3}{4}\) / Roots are equal and \(x=-\frac{3}{4}\)
Step 1
Concept
Here (16x-2 +24x+9=(4x+3)2 ). Hence the equal root is \(x=-\frac{3}{4}\).
Step 2
Why this answer is correct
The correct answer is A. मूल समान हैं और \(x=-\frac{3}{4}\) / Roots are equal and \(x=-\frac{3}{4}\). Here (16x-2 +24x+9=(4x+3)2 ). Hence the equal root is \(x=-\frac{3}{4}\).
Step 3
Exam Tip
यहाँ (16x-2 +24x+9=(4x+3)2 ) है। अतः समान मूल \(x=-\frac{3}{4}\) है।
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