If $α, β$ are the roots of the equation $2 x^{2} - 3 x - 6 = 0$ , find the equation whose roots are $α^{2} + 2$ and $β^{2} + 2$ .

(x - 1) (x - 2) = 0

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x^{2} - 6 x + 9 = 0

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4 x^{2} - 49 x + 118 = 0

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None of these

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Solution

The correct option is C $4 x^{2} - 49 x + 118 = 0$
$α + β = \frac{3}{2}$
And
$α . β = - 3$
Therefore,
$α^{2} + β^{2} = (α + β)^{2} - 2 α β$
$= \frac{9}{4} + 6$
$= \frac{33}{4}$
Hence, the equation will be
$x^{2} - (\frac{33}{4} + 4) x + (9 + 2 (\frac{33}{4} + 4) = 0$
$4 x^{2} - 49 x + 118 = 0$ .

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