The value of a for which the sum of the squares of the roots of the equation x2 - (a - 2)x-a-1 = 0 assumes the least value is (1) Zero (2) 1 (3) 2 (4) 3

$$\begin{gathered} 2² - \mathrm{px}-1+ \mathrm{p} =0 \\ \mathrm{x}+\mathrm{\beta }= \mathrm{p} ; \times \mathrm{\beta }=\mathrm{p}-1 \\ \mathrm{y}={\mathrm{x}}^2+{\mathrm{\beta }}^2 \\ ={(\mathrm{x}+\mathrm{\beta })}^2-2\mathrm{x\beta } ={\mathrm{p}}^2-2(\mathrm{p}-1)={\mathrm{p}}^2-2\mathrm{p}+2 \\ \frac{\mathrm{dy}}{\mathrm{dp}}=0 \\ \Rightarrow 2\mathrm{p}-2=0 \\ \Rightarrow \mathrm{p}=1 \\ \mathbf{\Rightarrow }\mathbf{for}\mathbf{ }\mathbf{p}\mathbf{=}\mathbf{1}\mathbf{ }\mathbf{the}\mathbf{ }\mathbf{sum}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{squares}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{given}\mathbf{ }\mathbf{equation}\mathbf{ }\mathbf{will}\mathbf{ }\mathbf{have}\mathbf{ }\mathbf{minimum}\mathbf{ }\mathbf{ }\mathbf{value} \end{gathered}$$