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.
If (0) is a root of \(2x^2+bx+c=0\), what must be the value of (c)?
A. (c=0)
(x=0) रखने पर (c=0) मिलना चाहिए। इसलिए शून्य मूल के लिए अचर पद शून्य होता है। / Putting (x=0) must give (c=0). Therefore the constant term is zero for a zero root.
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What is the product of roots of \(5x^2-2x-8=0\)?
C. \(-\frac{8}{5}\)
मूलों का गुणनफल \(\frac{c}{a}\) होता है। यहां \(\frac{-8}{5}\) सही है। / The product of roots is \(\frac{c}{a}\). Here \(\frac{-8}{5}\) is correct.
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What is the sum of roots of \(x^2+11x+30=0\)?
B. (-11)
मूलों का योग \(-\frac{b}{a}\) है। यहां योग (-11) होगा। / The sum of roots is \(-\frac{b}{a}\). Here the sum is (-11).
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Which equation has roots (5) and (-3)?
A. \(x^2-2x-15=0\)
मूल (5) और (-3) होने पर ((x-5)(x+3)=0) होगा। इसे खोलने पर \(x^2-2x-15=0\) मिलता है। / With roots (5) and (-3), we get ((x-5)(x+3)=0). Expanding it gives \(x^2-2x-15=0\).
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Which of the following values is a root of \(x^2+4x=0\)?
B. (-4)
(x-2+4x=x(x+4)) है। इसलिए मूल (0) और (-4) हैं। / (x-2+4x=x(x+4)). Therefore the roots are (0) and (-4).
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What are the roots of \(x^2-49=0\)?
A. (7) और (-7)(7) and (-7)
(x-2-49=(x-7)(x+7)) है। इसलिए मूल (7) और (-7) हैं। / (x-2-49=(x-7)(x+7)). Therefore the roots are (7) and (-7).
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Which statement is correct about the roots of \(7x^2=0\)?
A. (0) दोहराया हुआ मूल है(0) is a repeated root
\(7x^2=0\) से \(x^2=0\) मिलता है। इसलिए (0) दोहराया हुआ मूल है। / From \(7x^2=0\), we get \(x^2=0\). Therefore (0) is a repeated root.
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If (4) is a root of \(x^2+mx-20=0\), what is the value of (m)?
A. (1)
(x=4) रखने पर (16+4m-20=0) इसलिए (m=1)। पैरामीटर के लिए मूल को सीधे रखें। / Putting (x=4) gives (16+4m-20=0), so (m=1). For a parameter, substitute the root directly.
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If (x+5) is a factor of a quadratic polynomial, which root is certain?
B. (-5)
(x+5=0) करने पर (x=-5) मिलता है। इसलिए निश्चित मूल (-5) है। / Solving (x+5=0) gives (x=-5). Therefore the certain root is (-5).
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If the product of two real roots is positive and their sum is negative, how will both roots be?
B. दोनों ऋणात्मकBoth negative
गुणनफल धनात्मक होने पर दोनों मूलों का चिन्ह समान होता है। योग ऋणात्मक होने से दोनों मूल ऋणात्मक होंगे। / A positive product means both roots have the same sign. A negative sum means both roots are negative.
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If one root of \(x^2-9x+18=0\) is (3), what is the other root?
B. (6)
(x-2-9x+18=(x-3)(x-6)) है। इसलिए दूसरा मूल (6) है। / (x-2-9x+18=(x-3)(x-6)). Therefore the other root is (6).
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Which equation has roots (-2) and (6)?
A. \(x^2-4x-12=0\)
मूल (-2) और (6) होने पर ((x+2)(x-6)=0) होगा। इसे खोलने पर \(x^2-4x-12=0\) मिलता है। / With roots (-2) and (6), we get ((x+2)(x-6)=0). Expanding it gives \(x^2-4x-12=0\).
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What is the repeated root of \(x^2-8x+16=0\)?
A. (4)
(x-2-8x+16=(x-4)2) है। इसलिए दोहराया हुआ मूल (4) है। / (x-2-8x+16=(x-4)2). Therefore the repeated root is (4).
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What are the roots of \(3x^2-27=0\)?
A. (3) और (-3)(3) and (-3)
\(3x^2-27=0\) से \(x^2=9\) मिलता है। इसलिए \(x=\pm3\) है। / From \(3x^2-27=0\), we get \(x^2=9\). Therefore \(x=\pm3\).
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What are the roots of \(x^2=9x\)?
A. (0) और (9)(0) and (9)
\(x^2=9x\) को \(x^2-9x=0\) लिखें। फिर (x(x-9)=0) से मूल (0) और (9) मिलते हैं। / Write \(x^2=9x\) as \(x^2-9x=0\). Then (x(x-9)=0) gives roots (0) and (9).
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What are the roots of \(x^2-5x=0\)?
A. (0) और (5)(0) and (5)
(x-2-5x=x(x-5)) है। इसलिए मूल (0) और (5) हैं। / (x-2-5x=x(x-5)). Therefore the roots are (0) and (5).
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Which statement is correct about the real roots of \(x^2+9=0\)?
C. कोई वास्तविक मूल नहीं हैIt has no real roots
किसी वास्तविक (x) के लिए \(x^2\ge0\) होता है। इसलिए \(x^2+9=0\) वास्तविक संख्या से संतुष्ट नहीं होता। / For any real (x), \(x^2\ge0\). So \(x^2+9=0\) is not satisfied by any real number.
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In which condition does a quadratic equation have no real roots?
C. (D<0)
जब (D<0) होता है तब वास्तविक मूल नहीं होते। यह मूलों की प्रकृति का सीधा नियम है। / When (D<0), there are no real roots. This is a direct rule for the nature of roots.
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What is the discriminant (D) of \(x^2-2x+5=0\)?
C. (-16)
यहां \(D=b^2-4ac=4-20=-16\) है। इसलिए वास्तविक मूल नहीं होंगे। / Here \(D=b^2-4ac=4-20=-16\). Therefore there will be no real roots.
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If (D>0), how are the real roots of a quadratic equation?
B. दो भिन्न वास्तविक मूलTwo distinct real roots
(D>0) होने पर दो भिन्न वास्तविक मूल मिलते हैं। मूलों की प्रकृति जानने के लिए \(D=b^2-4ac\) देखें। / When (D>0), two distinct real roots are obtained. To know the nature of roots, check \(D=b^2-4ac\).
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What is the product of roots of \(4x^2+7x-3=0\)?
B. \(-\frac{3}{4}\)
मूलों का गुणनफल \(\frac{c}{a}\) होता है। यहां \(\frac{c}{a}=\frac{-3}{4}\) है। / The product of roots is \(\frac{c}{a}\). Here \(\frac{c}{a}=\frac{-3}{4}\).
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What is the sum of roots of \(3x^2-5x+2=0\)?
A. \(\frac{5}{3}\)
मूलों का योग \(-\frac{b}{a}\) होता है। यहां (a=3) और (b=-5) इसलिए योग \(\frac{5}{3}\) है। / The sum of roots is \(-\frac{b}{a}\). Here (a=3) and (b=-5), so the sum is \(\frac{5}{3}\).
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If (2) is a root of \(x^2+qx-10=0\), what is the value of (q)?
B. (3)
(x=2) रखने पर (4+2q-10=0) इसलिए (q=3)। दिए गए मूल को सीधे समीकरण में रखें। / Putting (x=2) gives (4+2q-10=0), so (q=3). Substitute the given root directly into the equation.
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Which equation has roots (0) and (-6)?
A. \(x^2+6x=0\)
मूल (0) और (-6) होने पर समीकरण (x(x+6)=0) होगा। इसे खोलने पर \(x^2+6x=0\) मिलता है। / With roots (0) and (-6), the equation is (x(x+6)=0). Expanding it gives \(x^2+6x=0\).
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What are the roots of \(x^2+9x+20=0\)?
A. (-4) और (-5)(-4) and (-5)
(x-2+9x+20=(x+4)(x+5)) है। इसलिए मूल (-4) और (-5) हैं। / (x-2+9x+20=(x+4)(x+5)). Therefore the roots are (-4) and (-5).
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What are the roots of \(x^2-7x+12=0\)?
A. (3) और (4)(3) and (4)
(x-2-7x+12=(x-3)(x-4)) है। इसलिए मूल (3) और (4) हैं। / (x-2-7x+12=(x-3)(x-4)). Therefore the roots are (3) and (4).
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What are the roots of \(x^2-25=0\)?
A. (5) और (-5)(5) and (-5)
(x-2-25=(x-5)(x+5)) है। इसलिए मूल (5) और (-5) हैं। / (x-2-25=(x-5)(x+5)). Therefore the roots are (5) and (-5).
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Is (x=-2) a root of \(x^2+3x+2=0\)?
A. हाँYes
(x=-2) रखने पर (4-6+2=0) मिलता है। ऋणात्मक मान रखते समय चिन्हों पर ध्यान दें। / Putting (x=-2) gives (4-6+2=0). Be careful with signs when substituting a negative value.
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Is (x=1) a root of \(x^2-3x+2=0\)?
A. हाँYes
(x=1) रखने पर (1-3+2=0) मिलता है। इसलिए (1) इसका मूल है। / Putting (x=1) gives (1-3+2=0). Therefore (1) is a root.
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A root of a quadratic equation (p(x)=0) is a number for which the value of (p(x)) becomes what?
B. (0)
मूल रखने पर (p(x)=0) बनता है। परीक्षा में मूल की जांच हमेशा प्रतिस्थापन से करें। / When a root is substituted, (p(x)=0) becomes true. In exams always check a root by substitution.
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