If $α$ and $β$ are the roots of the equation $x^{2} - 4 x + 2 = 0$ , find the value of $α^{2} + β^{2}$ .

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Solution

The correct option is C 12
The given equation is $x^{2} - 4 x + 2 = 0$ .....(1)
According to the problem, $α$ and $β$ are the roots of the equation 1.
Therefore,
$α + β = - \frac{b}{a} = - \frac{- 4}{1} = 4$

and $α β = \frac{c}{a} = \frac{2}{1} = 2$

Now, $α^{2} + β^{2} = (α + β)^{2} - 2 α β = (4)^{2} - 2 \times 2 = 16 - 4 = 12$

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