Question

Solve the given quadratic equation by factorization method
$x^2+3x-(a^2+a-2)=0$

Answer 1

We have
$x^2+3x-(a^2+a-2)=0$

$\Rightarrow x^2+3x-(a+2)(a-1)=0$

$\Rightarrow x^2+\left\{\right(a+2)-(a-1\left)\right\}x-(a+2)(a-1)=0$

$\Rightarrow \{x^2+(a+2\left)x\right\}-(a-1)x-(a+2)(a-1)=0$

$\Rightarrow \{x+(a+2\left)\right\}\{x-(a-1\left)\right\}=0$

$\Rightarrow x+(a+2)=0orx-(a-1)=0\Rightarrow x=-(a+2)orx=a-1$