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Inequalities Involving Modulus Function

If α, β are t...

Question

If $α, β$ are the roots of the equation $x^{2} + 3 x + 1 = 0$ , find the value of $(| (α - β) |)^{2}$

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Solution

$α + β = - 3$
$α β = 1$
$(α - β)^{2} = (α + β)^{2} - 4 α β$
=( $- 3)^{2}$ -4
=9 - 4
=5

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