Question

` x^2+6x-(a^2+2a-8)=0` 

Answer 1

We write,  

`6x=(a+4)x-(a-2) x` as 

`x^2xx[-(a^2a-8)]=-(a^2+2a-8)x^2=(a+4)x  xx[-(a-2)x]` 

∴`x^2+6x-(a^2+2a-8)=0` 

⇒`x^2+(a+4)x-(a-2)x(a+4)(a-2)=0` 

⇒`x[x+(a+4)]-(a-2)[x+(a+4)]=0` 

⇒`[x+(a+4)][x-(a-2)]=0` 

⇒`x+(a+4)=0  or  x-(a-2)=0` 

⇒`x=-(a+4)  or x= a-2` 

Hence, -(a+4) and (a-2) are the roots of the given equation.