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Factor Theorem

Let α,β be ...

Question

Let $α, β$ be the roots of the quadratic equation $a x^{2} + b x + c = 0$ . Then find the value of $\frac{1}{α} + \frac{1}{β}$ .

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Solution

Given, $α, β$ be the roots of the quadratic equation $a x^{2} + b x + c = 0$ .
Then from the relation between the roots and co-efficient we get,
$α + β = - \frac{b}{a}$ ......(1) and $α . β = \frac{c}{a}$ .......(2).
Then
$\frac{1}{α} + \frac{1}{β}$
$= \frac{α + β}{α . β}$
$= \frac{\frac{- b}{a}}{\frac{c}{a}}$ [ Using (1) and (2)]
$= - \frac{b}{c}$ .

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