The condition that one root of a x2-b x-c-0 is m times the other is -

The correct option is C mb2 = ac (m + 1)2 ax^2+ bx + c=0 let roots be α and αm α(1+m) = b/a , α^2m=c/a = gt; c/am =b^2/ a^2(m+1)^2 = gt; mb^2 =ac(m+ ...

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Standard X

Mathematics

Nature of Roots

The condition...

Question

The condition that one root of ax² + bx + c = 0 is m times the other is :

mc² = ab (m + 1)²

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mb² = ac (m + 1)²

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ma² = bc (m + 1)²

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None of these

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Solution

The correct option is B
mb² = ac (m + 1)²

a $x^{2}$ + bx + c=0

let roots be α and αm

α(1+m) = -b/a , $α^{2}$ m=c/a

=> c/am = $b^{2}$ / $a^{2}$ ${(m + 1)}^{2}$ => m $b^{2}$ =ac ${(m + 1)}^{2}$

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The condition that one root of ax2 + bx + c = 0 is m times the other is :

The correct option is B mb2 = ac (m + 1)2 ax2+ bx + c=0 let roots be α and αm α(1+m) = -b/a , α2m=c/a => c/am =b2/ a2(m+1)2 => mb2 =ac(m+1)2

The condition that one root of ax² + bx + c = 0 is m times the other is :

The correct option is B
mb² = ac (m + 1)²

a $x^{2}$ + bx + c=0

let roots be α and αm

α(1+m) = -b/a , $α^{2}$ m=c/a

=> c/am = $b^{2}$ / $a^{2}$ ${(m + 1)}^{2}$ => m $b^{2}$ =ac ${(m + 1)}^{2}$