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The value of ‘a’ for which the quadratic equation $2 x^{2} - x (a^{2} + 8 a - 1) + (a^{2} - 4 a) = 0$ has roots opposite signs, lie in the interval $(α, β)$ then $(α + 2 β) =$

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answer is D.

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Detailed Solution

$a = 2, b = - (a^{2} + 8 a - 1), c = a^{2} - 4 a \Rightarrow \frac{a^{2} - 4 a}{2} < 0 \Rightarrow a^{2} - 4 a < 0 \Rightarrow (a - 0) (a - 4) < 4 \Rightarrow 0 < a < 4 a \in (0, 4) α = 0, β = 4 α + 2 β = 0 + 2 (4) = 8$

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