If the roots of the equation ax2 - bx - c -0 be- and - then the roots of the equation cx2 - bx -a - 0 are

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 = a/c but α+β/αβ = b ...

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Byju's Answer

Standard XI

Mathematics

Transformation of Roots: Algebraic Transformation

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

$\frac{1}{α}, \frac{1}{β}$

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$- α, - β$

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$N o n e o f t h e s e$

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$α, \frac{1}{β}$

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Solution

The correct option is A
$\frac{1}{α}, \frac{1}{β}$

$α, β$ 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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