Question

`2x^2+ax-a^2=0`

Answer 1

We write, `ax=2ax-ax  as  2x^2xx(-a^2)=-2a^2x^2=2axx(-ax)` 

∴` 2x^2+ax-a^2=0` 

`⇒2x^2+2ax-ax-a^2=0` 

`⇒2x(x+a)-a(x+a)=0` 

`⇒(x+a)(2x-a)=0` 

`⇒x+a=0  or  2x-a=0` 

`⇒x=-a  or  x=a/2` 

Hence, -a  and ` a/2`are the roots of the given equation.