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Composite Function

The values of...

Question

The values of $: a^{'}$ for which the sum of roots of the equation $x^{2} + (2 - a - a^{2}) x - a^{2} = 0$ is zero are $α$ and $β$ then $| α + β | =$

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Solution

Given equation is $x^{2} + (2 - a - a^{2}) x - a^{2} = 0$
Sum of roots is $0$
$⟹ \frac{- (2 - a - a^{2})}{1} = 0$
$⟹ a^{2} + a - 2 = 0$
$⟹ a^{2} + 2 a - a - 2 = 0$
$⟹ a (a + 2) - (a + 2) = 0$
$⟹ (a - 1) (a + 2) = 0$
$⟹ a = 1, - 2$
So $α = 1, β = - 2$
$| α + β | = | 1 - 2 | = | - 1 | = 1$

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