Short-Answer Questions

$x^{2}+5 x-\left(a^{2}+a-6\right)=0$

$\Rightarrow x^{2}+5 x-(a+3)(a-2)=0$

$\Rightarrow x^{2}+[(a+3)-(a-2)] x-(a+3)(a-2)=0$

$\Rightarrow x^{2}+(a+3) x-(a-2) x-(a+3)(a-2)=0$

$\Rightarrow x[x+(a+3)]-(a-2)[x+(a+3)]=0$

$\Rightarrow[x+(a+3)][x-(a-2)]=0$

$\Rightarrow x+(a+3)=0$ or $x-(a-2)=0$

$\Rightarrow x=-(a+3)$ or $x=(a-2)$

Hence, $-(a+3)$ and $(a-2)$ are the roots of the given equation.