Question:
Short-Answer Questions
Solve: $x^{2}+5 x-\left(a^{2}+a-6\right)=0$
Solution:
$x^{2}+5 x-\left(a^{2}+a-6\right)=0$
$\Rightarrow x^{2}+5 x-(a+3)(a-2)=0$
$\Rightarrow x^{2}+[(a+3)-(a-2)] x-(a+3)(a-2)=0$
$\Rightarrow x^{2}+(a+3) x-(a-2) x-(a+3)(a-2)=0$
$\Rightarrow x[x+(a+3)]-(a-2)[x+(a+3)]=0$
$\Rightarrow[x+(a+3)][x-(a-2)]=0$
$\Rightarrow x+(a+3)=0$ 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.
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