If $α, β$ are the roots of the equation $x^{2} + 2 x - 15 = 0$ then find the values of $α^{2} + β^{2}$

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Solution

Here $a = 1, b = 2, c = - 15$

Sum of the roots $= \frac{- b}{a} = \frac{- 2}{1} = - 2$

Product of the roots $= \frac{c}{a} = \frac{- 15}{1} = - 15$

$α^{2} + β^{2} = {(α + β)}^{2} - 2 α β$

$= {(- 2)}^{2} - 2 \times - 15$

$= 4 + 30 = 34$

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