Question:medium

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?

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For quadratic root expressions: \begin{itemize} \item Use identities: \[ \alpha^2+\beta^2 = (\alpha+\beta)^2 - 2\alpha\beta \] \item Convert into quadratic in parameter and minimize. \end{itemize}

Updated On: Mar 2, 2026

\( 2 \)
\( 0 \)
\( 3 \)
\( 1 \)

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The Correct Option is D

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The Correct Option is D

Solution and Explanation

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