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Relation between Roots and Coefficients for Quadratic

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Question

Find the value of $α^{2} + β^{2}$ if $α, β$ are the roots of $x^{2} + 5 x + 2 = 0$

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Solution

Given: $x^{2} + 5 x + 2 = 0$
$α + β = - 5$

$α β = 2$

$α^{2} + β^{2} = (α + β)^{2} - 2 α β$

$= (- 5)^{2} - 2 \times 2$

$= 25 - 4$

$= 21$

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