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?
Show Hint
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}