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If $α, β, γ$ are the roots of $2 x^{3} + 5 x^{2} - 3 x + 1 = 0$ then the equation whose roots are $\frac{α}{2}, \frac{β}{2}, \frac{γ}{2}$ is

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$16 x^{3} + 20 x^{2} + 6 x + 1 = 0$

$16 x^{3} + 20 x^{2} - 6 x - 1 = 0$

$16 x^{3} - 20 x^{2} - 6 x + 1 = 0$

$16 x^{3} + 20 x^{2} - 6 x + 1 = 0$

answer is A.

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Detailed Solution

$f (2 x) = 0$ (roots are multiplied by 1/k then the equation is f(kx)=0)

$\Rightarrow 16 x^{3} + 20 x^{2} - 6 x + 1 = 0$

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