Question

Solve the given quadratic equation by factorization method
$x^2+x-(a+1)(a+2)=0$

Answer 1

We have
$x^2+x-(a+1)(a+2)=0$

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

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

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