Question

Solve `x^2+5x-(a^2+a-6)=0` 

 

Answer 1

`x^2+5x-(a^2+a-6)=0` 

⇒`x^2+5x-(a+3)(a-2)=0` 

⇒`x^2+[(a+3)-(a-2)]x-(a+3)(a-2)=0` 

⇒`x^2+(a+3)x(a-2)x-(a+3)(a-2)=0` 

⇒`x[x+(x+3)]-(a-2) [x+(a+3)]=0` 

⇒`[x+(a+3)] [x-(a-2)]=0` 

⇒`x+(a+3)=0  or  x-(a-2)=0` 

⇒`x=-(a+3)  or  x=(a-2)` 

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