If α and β are the roots of the equation ax2+bx+c=0 , then 1aα+b+1aβ+b is equal to

α+β=−ba∴aα+b=−aβ and aβ+b=−aα ∴S=−1a(α+βαβ)=−1a(−b/ac/a)=bac

If α and β are the roots of the equation ax2+bx+c=0 , then 1aα+b+1aβ+b is equal to

α+β=−ba∴aα+b=−aβ and aβ+b=−aα ∴S=−1a(α+βαβ)=−1a(−b/ac/a)=bac

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If $α$ and $β$ are the roots of the equation $a x^{2} + b x + c = 0$ , then $\frac{1}{a α + b} + \frac{1}{a β + b}$ is equal to

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$\frac{- a c}{b}$

$\frac{a c}{b}$

$\frac{b}{a c}$

$\frac{- b}{a c}$

answer is A.

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Detailed Solution

$α + β = \frac{- b}{a}$
$∴ a α + b = - a β$ and $a β + b = - a α$
$∴ S = \frac{- 1}{a} (\frac{α + β}{α β}) = \frac{- 1}{a} (\frac{- b / a}{c / a}) = \frac{b}{a c}$

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If α and β are the roots of the equation ax2+bx+c=0 , then 1aα+b+1aβ+b is equal to

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If $α$ and $β$ are the roots of the equation $a x^{2} + b x + c = 0$ , then $\frac{1}{a α + b} + \frac{1}{a β + b}$ is equal to