If the roots of the equation a x2-b x-c-0 be - and - then the roots of the equation c x2-b x-a-0 are

The correct option is C α, β are roots of ax^2 + bx + c =0 ⇒ α+β= b/a and αβ =c/a Let the roots of cx^2 + bx + a = 0 be α',β', then α ' + β '= b/c and α β ...

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Byju's Answer

Standard XI

Mathematics

Inequalities Involving Modulus Function

If the roots ...

Question

If the roots of the equation $a x^{2} + b x + c = 0$ be $α a n d β$ ,, then the roots of the equation $c x^{2} + b x + a = 0$ are

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Solution

The correct option is C

$α, β$ are roots of $a x^{2} + b x + c = 0$

$\Rightarrow α + β$ = $- \frac{b}{a} a n d α β = \frac{c}{a}$

Let the roots of $c x^{2} + b x + a = 0$ be $α$ ', $β$ ', then

$α$ ' + $β$ ' $= - \frac{b}{c} a n d α β = \frac{a}{c}$

but $\frac{α + β}{α β} = \frac{- \frac{b}{a}}{\frac{c}{a}} = \frac{- b}{c} \frac{1}{α} + \frac{1}{β} = α^{'} + β^{'}$

Hence $α^{'} = \frac{1}{α} a n d β^{'} = \frac{1}{β}$

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If the roots of the equation ax2+bx+c=0 beα and β,, then the roots of the equation cx2+bx+a=0 are

The correct option is C α,β are roots of ax2+bx+c=0 ⇒ α+β= −ba and αβ=ca Let the roots of cx2+bx+a=0 be α',β', then α ' + β '=−bc and α β=ac but α+βαβ=−baca=−bc1α+1β=α′+β′ Hence α′=1α and β′=1β

If the roots of the equation $a x^{2} + b x + c = 0$ be $α a n d β$ ,, then the roots of the equation $c x^{2} + b x + a = 0$ are