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If $\cos^{4} θ + α, \sin^{4} θ + α$ are the roots of the equation $x^{2} + 2 b x + b = 0$ and $\cos^{2} θ + β, \sin^{2} θ + β$ are the roots of $x^{2} + 4 x + 2 = 0$ the value of b is

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answer is C.

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Detailed Solution

Difference of roots of given equations is same

$\Rightarrow \frac{\sqrt{Δ}}{| a |} = \frac{\sqrt{Δ}}{| a |} \Rightarrow 4 b^{2} - 4 b = 16 - 8$

$\Rightarrow b^{2} - b - 2 = 0 \Rightarrow b = - 1, 2$

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