Q63 / 155 · WBJEE 2025 · Mathematics

For what value of ' $a$ ', the sum of the squares of the roots of the equation $x^2-(a-2) x-a+1=0$ will have the least value?

A
$2$
B
$0$
C
$3$
Correct answer
D
$1$

Solution

$\begin{aligned} & \alpha^2+\beta^2=(\alpha+\beta)^2-2 \alpha \beta \\ & =(a-2)^2-2(1-a) \\ & =a^2-4 a+4-2+2 a \\ & =a^2-2 a+2 \\ & =(a-1)^2+1\end{aligned}$

Hence, the correct answer is option: 'D'.

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