roots se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.
657 questions tagged with roots.
What are the roots of \(x^2-6x+9=0\)?
A. (3) और (3)(3) and (3)
(x-2-6x+9=(x-3)2) है। इसलिए दोनों मूल (3) हैं। / (x-2-6x+9=(x-3)2). Therefore both roots are (3).
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If (4) is a root of \(2x^2-9x+n=0\), what is the value of (n)?
B. (4)
(x=4) रखने पर (32-36+n=0) इसलिए (n=4)। गणना में हर पद अलग अलग निकालें। / Putting (x=4) gives (32-36+n=0), so (n=4). Calculate each term separately.
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Which monic quadratic equation has sum of roots (10) and product of roots (21)?
B. \(x^2-10x+21=0\)
\(मोनिक समीकरण (x^2-(\)योग)x+गुणनफल=0) होता है। इसलिए \(x^2-10x+21=0\) सही है। \(/ A monic equation is (x^2-(\)sum)x+product\(=0). Therefore (x^2-10x+21=0) is correct.\)
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If the roots of an equation are (4) and (-7), what is their sum?
B. (-3)
योग (4+(-7)=-3) है। ऋणात्मक संख्या जोड़ते समय चिन्ह का ध्यान रखें। / The sum is (4+(-7)=-3). Be careful with the sign while adding a negative number.
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If ((x-4)(x+9)=0), what are the roots?
C. (4) और (-9)(4) and (-9)
शून्य गुणनफल नियम से (x-4=0) या (x+9=0) होगा। इसलिए मूल (4) और (-9) हैं। / By the zero product rule, (x-4=0) or (x+9=0). Therefore the roots are (4) and (-9).
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Which of the following values is not a root of \(x^2-100=0\)?
C. (0)
\(x^2-100=0\) के मूल (10) और (-10) हैं। (0) रखने पर समीकरण सत्य नहीं होता। / The roots of \(x^2-100=0\) are (10) and (-10). Substituting (0) does not make the equation true.
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Which is the root of \(x^2-18x+81=0\)?
A. (9) दो बार(9) twice
(x-2-18x+81=(x-9)2) है। इसलिए दोहराया मूल (9) है। / (x-2-18x+81=(x-9)2). Therefore the repeated root is (9).
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What are the roots of \(4x^2-20x=0\)?
A. (0) और (5)(0) and (5)
(4x-2-20x=4x(x-5)) है। इसलिए मूल (0) और (5) हैं। / (4x-2-20x=4x(x-5)). Therefore the roots are (0) and (5).
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What are the roots of \(x^2+16x+64=0\)?
B. (-8) और (-8)(-8) and (-8)
(x-2+16x+64=(x+8)2) है। इसलिए दोनों मूल (-8) हैं। / (x-2+16x+64=(x+8)2). Therefore both roots are (-8).
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If (-3) is a root of \(x^2+ux-18=0\), what is the value of (u)?
A. (-9)
(x=-3) रखने पर (9-3u-18=0) इसलिए (u=-3) नहीं बल्कि (u=-3)? / Putting (x=-3) gives (9-3u-18=0), so (u=-3), not (u=3).
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If (0) is a root of \(5x^2+kx+c=0\), which term must be zero?
A. अचर पद (c)Constant term (c)
(x=0) रखने पर केवल (c) बचता है। इसलिए शून्य मूल के लिए (c=0) होना चाहिए। / Putting (x=0) leaves only (c). Therefore for a zero root, (c=0) must hold.
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What is the product of roots of \(7x^2+5x-14=0\)?
B. (-2)
मूलों का गुणनफल \(\frac{c}{a}\) होता है। यहां \(\frac{-14}{7}=-2\) है। / The product of roots is \(\frac{c}{a}\). Here \(\frac{-14}{7}=-2\).
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What is the sum of roots of \(x^2-13x+42=0\)?
A. (13)
मूलों का योग \(-\frac{b}{a}\) है। यहां (b=-13) इसलिए योग (13) है। / The sum of roots is \(-\frac{b}{a}\). Here (b=-13), so the sum is (13).
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Which equation has roots (6) and (-2)?
A. \(x^2-4x-12=0\)
मूल (6) और (-2) होने पर ((x-6)(x+2)=0) होगा। इसे खोलने पर \(x^2-4x-12=0\) मिलता है। / With roots (6) and (-2), we get ((x-6)(x+2)=0). Expanding it gives \(x^2-4x-12=0\).
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Which of the following values is a root of \(x^2-9x=0\)?
C. (9)
(x-2-9x=x(x-9)) है। इसलिए मूल (0) और (9) हैं। / (x-2-9x=x(x-9)). Therefore the roots are (0) and (9).
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What are the roots of \(x^2-81=0\)?
A. (9) और (-9)(9) and (-9)
(x-2-81=(x-9)(x+9)) है। इसलिए मूल (9) और (-9) हैं। / (x-2-81=(x-9)(x+9)). Therefore the roots are (9) and (-9).
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Which statement is correct about the roots of \(11x^2=0\)?
A. (0) दोहराया हुआ मूल है(0) is a repeated root
\(11x^2=0\) से \(x^2=0\) मिलता है। इसलिए (0) दोहराया हुआ मूल है। / From \(11x^2=0\), we get \(x^2=0\). Therefore (0) is a repeated root.
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If (5) is a root of \(x^2+tx-30=0\), what is the value of (t)?
A. (1)
(x=5) रखने पर (25+5t-30=0) इसलिए (t=1)। मूल ज्ञात हो तो सीधे प्रतिस्थापन करें। / Putting (x=5) gives (25+5t-30=0), so (t=1). If the root is known, substitute directly.
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If (x-9) is a factor of a quadratic polynomial, which root is certain?
A. (9)
(x-9=0) करने पर (x=9) मिलता है। इसलिए निश्चित मूल (9) है। / Solving (x-9=0) gives (x=9). Therefore the certain root is (9).
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If the product of two real roots is positive and their sum is positive, how will both roots be?
A. दोनों धनात्मकBoth positive
गुणनफल धनात्मक होने पर दोनों चिन्ह समान होते हैं। योग धनात्मक होने से दोनों मूल धनात्मक होंगे। / A positive product means both signs are same. A positive sum means both roots are positive.
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If one root of \(x^2-11x+30=0\) is (5), what is the other root?
B. (6)
(x-2-11x+30=(x-5)(x-6)) है। इसलिए दूसरा मूल (6) है। / (x-2-11x+30=(x-5)(x-6)). Therefore the other root is (6).
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Which equation has roots (-4) and (2)?
A. \(x^2+2x-8=0\)
मूल (-4) और (2) होने पर ((x+4)(x-2)=0) होगा। इसे खोलने पर \(x^2+2x-8=0\) मिलता है। / With roots (-4) and (2), we get ((x+4)(x-2)=0). Expanding it gives \(x^2+2x-8=0\).
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What is the repeated root of \(x^2-12x+36=0\)?
A. (6)
(x-2-12x+36=(x-6)2) है। इसलिए दोहराया हुआ मूल (6) है। / (x-2-12x+36=(x-6)2). Therefore the repeated root is (6).
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What are the roots of \(5x^2-45=0\)?
A. (3) और (-3)(3) and (-3)
\(5x^2-45=0\) से \(x^2=9\) मिलता है। इसलिए \(x=\pm3\) है। / From \(5x^2-45=0\), we get \(x^2=9\). Therefore \(x=\pm3\).
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What are the roots of \(x^2=4x\)?
A. (0) और (4)(0) and (4)
\(x^2=4x\) को \(x^2-4x=0\) लिखें। फिर (x(x-4)=0) से मूल (0) और (4) मिलते हैं। / Write \(x^2=4x\) as \(x^2-4x=0\). Then (x(x-4)=0) gives roots (0) and (4).
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What are the roots of \(x^2+6x=0\)?
A. (0) और (-6)(0) and (-6)
(x-2+6x=x(x+6)) है। इसलिए मूल (0) और (-6) हैं। / (x-2+6x=x(x+6)). Therefore the roots are (0) and (-6).
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Which statement is correct about the real roots of \(x^2+25=0\)?
C. कोई वास्तविक मूल नहीं हैIt has no real roots
वास्तविक (x) के लिए \(x^2\ge0\) होता है। इसलिए \(x^2+25=0\) का कोई वास्तविक मूल नहीं है। / For real (x), \(x^2\ge0\). Therefore \(x^2+25=0\) has no real root.
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In which condition does a quadratic equation have two distinct real roots?
C. (D>0)
दो भिन्न वास्तविक मूलों के लिए (D>0) होना चाहिए। यह प्रकृति जांचने का सीधा नियम है। / For two distinct real roots, (D>0) is required. This is a direct rule to check the nature.
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What is the discriminant (D) of \(x^2+4x+4=0\)?
B. (0)
यहां \(D=b^2-4ac=16-16=0\) है। इसलिए दोनों मूल बराबर होंगे। / Here \(D=b^2-4ac=16-16=0\). Therefore the two roots will be equal.
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If (D=0), how are the real roots of a quadratic equation?
B. दो बराबर वास्तविक मूलTwo equal real roots
(D=0) होने पर दोनों वास्तविक मूल बराबर होते हैं। मूलों की प्रकृति के लिए \(D=b^2-4ac\) देखें। / When (D=0), the two real roots are equal. Check \(D=b^2-4ac\) for the nature of roots.
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