If the sum of the squares of the roots of the equation $x^2-(a-2) x-(a+1)=0$ is least for an appropriate value of the variable parameter $a$, then that value of ' $a$ ' will be

If $$\mathrm{P}(x)=\mathrm{a} x^2+\mathrm{b} x+\mathrm{c}$$ and $$\mathrm{Q}(x)=-\mathrm{a} x^2+\mathrm{d} x+\mathrm{c}$$ where $$\mathrm{ac} \neq 0$$, then $$\mathrm{P}(x) \cdot \mathrm{Q}(x)=0$$ has (a, b, c, d are real)