If $α$ and $β$ are the roots of the equation $x^{2} + 5 x + 5 = 0$ , find the value of $α^{- 1} + β^{- 1}$ .

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Solution

Let, $α$ and $β$ are the roots of the equation $x^{2} + 5 x + 5 = 0$ , then the relation between the roots and co-efficients we get,
$α + β = - 5$ and $α . β = 5$ .......(1).
Now,
$α^{- 1} + β^{- 1}$
$= \frac{1}{α} + \frac{1}{β}$
$= \frac{α + β}{α . β}$
$= - 1$ [ Using (1)]

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