If α and β are the roots of the equation $2 x^{2} - 3 x + 4 = 0$ , then the equation whose roots are $α^{2}$ and $β^{2}$ is

$4 x^{2} + 7 x + 16 = 0$

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$4 x^{2} + 7 x + 6 = 0$

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$4 x^{2} + 7 x + 1 = 0$

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$4 x^{2} - 7 x + 16 = 0$

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Solution

The correct option is A
$4 x^{2} + 7 x + 16 = 0$

α + β = $\frac{3}{2}$ and αβ = 2

$α^{2} + β^{2} = (α + β)^{2} - 2 α β = \frac{9}{4} - 4 = - \frac{7}{4}$

hence required equation $x^{2} - (α^{2} + β^{2}) x + α^{2} β^{2} = 0$

⇒ $x^{2} + \frac{7}{4} x + 4 = 0$ ⇒ $4 x^{2} + 7 x + 16 = 0$

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