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Standard X

Mathematics

Roots of Quadratic Equation

Let α,β be ...

Question

Let $α, β$ be the roots of the quadratic equation $p x^{2} + q x + r = 0$ 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 $p x^{2} + q x + r = 0$ .
Then from the relation between roots and co-efficients we get,
$α + β = - \frac{q}{p}$ .....(1) and $α . β = \frac{r}{p}$ ......(2).
Now,
$\frac{1}{α} + \frac{1}{β}$
$= \frac{α + β}{α . β}$
$= - \frac{q}{r}$ . [ Using (1) and (2)]

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