If $α$ a root of the equation $2 x (2 x + 1) = 1,$ then the other root is

- 2 α (α + 1)

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3 α^{3} - 4 α

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3 α - 4 α^{3}

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none of these

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Solution

The correct option is D none of these
Roots of the given equation $4 x^{2} + 2 x - 1 = 0$ are;

$\Rightarrow \frac{\sqrt{5} - 1}{4} a n d - \frac{(\sqrt{5} + 1)}{4}$

Which are equivalent to cos72 and - cos36

Let $c o s 72 = α$

Now - cos36=cos(36+180)=cos216

$\Rightarrow c o s 216 = c o s (3 \times 72) = 4 c o s^{3} 72 - 3 c o s 72$

$∴ o t h e r r o o t = c o s 216 = 4 α^{3} - 3 α$

Hence answer is $4 α^{3} - 3 α$

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