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Q.

If $α, β$ are the roots of the equation $x^{2} - 2 x - a^{2} + 1 = 0$ and $γ, δ$ are the roots of
The equation $x^{2} - 2 (a + 1) x + a (a - 1) = 0$ such that $α, β \in (γ, δ)$ , then the set of all possible values of a can lie in

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a

$(- \infty, - 2)$

b

$(- \infty, 1)$

c

$(- \frac{1}{4}, 1)$

d

$(- \frac{1}{8}, \frac{1}{2})$

answer is A, C.

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Detailed Solution

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$x^{2} - 2 x - (a^{2} - 1) = 0 \Rightarrow x = a - 1, a + 1$
$f (x) = x^{2} - 2 (a + 1) x + a (a - 1)$
Question Image
$f (a - 1) < 0, f (a + 1) < 0.$

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If α,β are the roots of the equation x2-2x-a2+1=0 and γ,δ are the roots of The equation x2−2(a+1)x+a(a−1)=0 such that α,β∈(γ,δ) , then the set of all possible values of a can lie in