Question

`x^2+5x-(a^2+a-6)=0` 

Answer 1

We write, 5x=(a+3)x-(a-2)x as  

`x^2xx[-(a^2+a-6)]=-(a^2+a-6)x^2=(a+3)x xx[-(a-2)x]` 

∴`x^2+5x(a^2+a-6)=0` 

`⇒x^2+(a+3)x-(a-2)x-(a+3)(a-2)=0` 

`⇒x[x+(a+3)]-(a-2)[x+(a+3)]=0` 

⇒`  [x+(a+3)][x-(a-2)=0]` 

⇒`x+(a+3)=0   x-(a-2)=0` 

⇒` x=-(a+3) or  x=a-2` 

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