The value of $\alpha$ for which the sum of the squares of the roots of the equation $x^2-(a-2) x-a-1=0$ assume the least value is

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Aicharya · Accepted Answer

$ \begin{aligned} & x^2-(a-2) x-a-1=0 \ & \Rightarrow \alpha+\beta=a-2 \ & \alpha \beta=-(a+1) \ & \alpha^2+\beta^2=(\alpha+\beta)^2-2 \alpha \beta \ & \quad=a^2-2 a+6=(a-1)^2+5 \ & \Rightarrow a=1 . \end{aligned} $

The value of $\alpha$ for which the sum of the squares of the roots of the equation $x^2-(a-2) x-a-1=0$…

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