If $α, β$ and $γ$ are the roots of $x^{3} + 8 = 0$ , then the equation whose roots are $α^{2}, β^{2} a n d γ^{2}$ is

$x^{3} - 8 = 0$

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$x^{3} - 16 = 0$

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$x^{3} + 64 = 0$

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$x^{3} - 64 = 0$

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Solution

The correct option is D
$x^{3} - 64 = 0$

Let $y = x^{2}$ . then $x = \sqrt{y}$

∴ $x^{3} + 8 = 0$ ⇒ $y^{\frac{3}{2}} + 8 = 0$

⇒ $y^{3} = 64$ ⇒ $y^{3} - 64 = 0$

Thus the equation having roots $α^{2}, β^{2}$ and $γ^{2} i s x^{3} - 64 = 0$

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