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 is the product of roots of \(6x^2-x-2=0\)?
A. \(-\frac{1}{3}\)
मूलों का गुणनफल \(\frac{c}{a}\) होता है। यहां \(\frac{-2}{6}=-\frac{1}{3}\) सही है। / The product of roots is \(\frac{c}{a}\). Here \(\frac{-2}{6}=-\frac{1}{3}\) is correct.
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What is the sum of roots of \(2x^2+3x-5=0\)?
A. \(-\frac{3}{2}\)
मूलों का योग \(-\frac{b}{a}\) होता है। यहां योग \(-\frac{3}{2}\) है। / The sum of roots is \(-\frac{b}{a}\). Here the sum is \(-\frac{3}{2}\).
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If (3) is a root of \(x^2+sx-12=0\), what is the value of (s)?
A. (1)
(x=3) रखने पर (9+3s-12=0) इसलिए (s=1)। दिए गए मूल को सीधे समीकरण में रखें। / Putting (x=3) gives (9+3s-12=0), so (s=1). Substitute the given root directly into the equation.
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Which equation has roots (0) and (8)?
A. \(x^2-8x=0\)
मूल (0) और (8) होने पर समीकरण (x(x-8)=0) होगा। इसे खोलने पर \(x^2-8x=0\) मिलता है। / With roots (0) and (8), the equation is (x(x-8)=0). Expanding it gives \(x^2-8x=0\).
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What are the roots of \(x^2+10x+21=0\)?
A. (-3) और (-7)(-3) and (-7)
(x-2+10x+21=(x+3)(x+7)) है। इसलिए मूल (-3) और (-7) हैं। / (x-2+10x+21=(x+3)(x+7)). Therefore the roots are (-3) and (-7).
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What are the roots of \(x^2-8x+15=0\)?
A. (3) और (5)(3) and (5)
(x-2-8x+15=(x-3)(x-5)) है। इसलिए मूल (3) और (5) हैं। / (x-2-8x+15=(x-3)(x-5)). Therefore the roots are (3) and (5).
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What are the roots of \(x^2-36=0\)?
A. (6) और (-6)(6) and (-6)
(x-2-36=(x-6)(x+6)) है। इसलिए मूल (6) और (-6) हैं। / (x-2-36=(x-6)(x+6)). Therefore the roots are (6) and (-6).
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Is (x=-1) a root of \(2x^2+x-1=0\)?
A. हाँYes
(x=-1) रखने पर (2-1-1=0) मिलता है। ऋणात्मक मूल में चिन्हों की जांच जरूरी है। / Putting (x=-1) gives (2-1-1=0). Sign checking is important with a negative root.
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Is (x=2) a root of \(x^2-4x+4=0\)?
A. हाँYes
(x=2) रखने पर (4-8+4=0) मिलता है। इसलिए (2) इसका मूल है। / Putting (x=2) gives (4-8+4=0). Therefore (2) is a root.
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If (p(a)=0) for a number (a), what is (a) called for (p(x)=0)?
A. मूलRoot
(p(a)=0) होने पर (a) समीकरण को संतुष्ट करता है। इसलिए (a) उसका मूल है। / If (p(a)=0), then (a) satisfies the equation. Therefore (a) is its root.
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If \(x=\frac{1}{2}\) is a root of \(4x^2+px-3=0\), what is the value of (p)?
B. (4)
\(x=\frac{1}{2}\) रखने पर \(1+\frac{p}{2}-3=0\) इसलिए (p=4)। भिन्न मूल रखते समय हर पद सावधानी से हल करें। / Putting \(x=\frac{1}{2}\) gives \(1+\frac{p}{2}-3=0\), so (p=4). When substituting a fractional root, solve each term carefully.
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If both roots of a monic quadratic equation are (-4) and (-4), which equation is it?
A. \(x^2+8x+16=0\)
दोनों मूल (-4) हों तो समीकरण ((x+4)2=0) होगा। इसे खोलने पर \(x^2+8x+16=0\) मिलता है। / If both roots are (-4), the equation is ((x+4)2=0). Expanding it gives \(x^2+8x+16=0\).
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What are the roots of \(3x^2-10x+3=0\)?
A. (3) और \(\frac{1}{3}\)(3) and \(\frac{1}{3}\)
(3x-2-10x+3=(3x-1)(x-3)) है। इसलिए मूल \(\frac{1}{3}\) और (3) हैं। / (3x-2-10x+3=(3x-1)(x-3)). Therefore the roots are \(\frac{1}{3}\) and (3).
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If the roots of a quadratic equation are (r) and (-r), what is their sum?
C. (0)
(r+(-r)=0) होता है। विपरीत मूलों का योग हमेशा (0) होता है। / (r+(-r)=0). The sum of opposite roots is always (0).
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If the sum of roots is (8) and one root is (3), what is the other root?
B. (5)
दूसरा मूल (8-3=5) है। योग में से दिया हुआ मूल घटाएं। / The other root is (8-3=5). Subtract the given root from the sum.
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If one root is (5) and the product of roots is (35), what is the other root?
B. (7)
दूसरा मूल \(\frac{35}{5}=7\) होगा। गुणनफल में दिए हुए मूल से भाग करें। / The other root is \(\frac{35}{5}=7\). Divide the product by the given root.
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What are the roots of \(x^2=49\)?
A. (7) और (-7)(7) and (-7)
\(x^2=49\) से \(x=\pm7\) मिलता है। वर्गमूल लेते समय दोनों चिन्ह लें। / From \(x^2=49\), we get \(x=\pm7\). Take both signs while finding square roots.
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What are the roots of \(x^2-3x-10=0\)?
A. (5) और (-2)(5) and (-2)
(x-2-3x-10=(x-5)(x+2)) है। इसलिए मूल (5) और (-2) हैं। / (x-2-3x-10=(x-5)(x+2)). Therefore the roots are (5) and (-2).
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How many real roots does \(x^2+16=0\) have?
C. (0)
वास्तविक संख्या के लिए \(x^2\ge0\) होता है। इसलिए \(x^2+16=0\) का कोई वास्तविक मूल नहीं है। / For a real number, \(x^2\ge0\). Therefore \(x^2+16=0\) has no real root.
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If (-3) is a root of a quadratic polynomial, which factor is certain?
B. (x+3)
मूल (r) होने पर गुणनखंड (x-r) होता है। (r=-3) के लिए गुणनखंड (x+3) होगा। / If the root is (r), the factor is (x-r). For (r=-3), the factor is (x+3).
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What are the roots of \(x^2-5x+6=0\)?
A. (2) और (3)(2) and (3)
(x-2-5x+6=(x-2)(x-3)) है। इसलिए मूल (2) और (3) हैं। / (x-2-5x+6=(x-2)(x-3)). Therefore the roots are (2) and (3).
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If (2) is a root of \(3x^2-8x+n=0\), what is the value of (n)?
B. (4)
(x=2) रखने पर (12-16+n=0) इसलिए (n=4)। ऐसे प्रश्नों में गणना धीरे और सही करें। / Putting (x=2) gives (12-16+n=0), so (n=4). In such questions calculate slowly and correctly.
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Which monic quadratic equation has sum of roots (-9) and product of roots (20)?
A. \(x^2+9x+20=0\)
\(मोनिक समीकरण (x^2-(\)योग)x+गुणनफल=0) होता है। इसलिए \(x^2+9x+20=0\) सही है। \(/ A monic equation is (x^2-(\)sum)x+product\(=0). Therefore (x^2+9x+20=0) is correct.\)
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If the roots of an equation are (2) and (-5), what is their sum?
B. (-3)
योग (2+(-5)=-3) है। ऋणात्मक मूल जोड़ते समय चिन्ह न भूलें। / The sum is (2+(-5)=-3). Do not forget the sign while adding a negative root.
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If ((x+1)(x-8)=0), what are the roots?
B. (-1) और (8)(-1) and (8)
शून्य गुणनफल नियम से (x+1=0) या (x-8=0) होगा। इसलिए मूल (-1) और (8) हैं। / By the zero product rule, (x+1=0) or (x-8=0). Therefore the roots are (-1) and (8).
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Which of the following values is not a root of \(x^2-64=0\)?
C. (0)
\(x^2-64=0\) के मूल (8) और (-8) हैं। (0) रखने पर समीकरण सत्य नहीं होता। / The roots of \(x^2-64=0\) are (8) and (-8). Substituting (0) does not make the equation true.
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Which is the root of \(x^2+14x+49=0\)?
B. (-7) दो बार(-7) twice
(x-2+14x+49=(x+7)2) है। इसलिए दोहराया मूल (-7) है। / (x-2+14x+49=(x+7)2). Therefore the repeated root is (-7).
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What are the roots of \(2x^2-10x=0\)?
A. (0) और (5)(0) and (5)
(2x-2-10x=2x(x-5)) है। इसलिए मूल (0) और (5) हैं। / (2x-2-10x=2x(x-5)). Therefore the roots are (0) and (5).
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What are the roots of \(x^2+12x+36=0\)?
B. (-6) और (-6)(-6) and (-6)
(x-2+12x+36=(x+6)2) है। इसलिए दोनों मूल (-6) हैं। / (x-2+12x+36=(x+6)2). Therefore both roots are (-6).
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If (-1) is a root of \(x^2+rx-12=0\), what is the value of (r)?
A. (-11)
(x=-1) रखने पर (1-r-12=0) इसलिए (r=-11)। ऋणात्मक मूल रखते समय प्रत्येक पद का चिन्ह देखें। / Putting (x=-1) gives (1-r-12=0), so (r=-11). Check the sign of each term while using a negative root.
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