Question

`4x^2-2(a^2+b^2)x+a^2b^2=0` 

 

Answer 1

`4x^2-2(a^2+b^2)x+a^2b^2=0` 

⇒`4x^2-2a^2x-2b^2x+a^2b^2=0` 

⇒`2x(2x-a^2)-b^2(2x-a^2)=0` 

⇒`(2x-b^2) (2x-a^2)=0` 

⇒`2x-b^2=0   or  2x-a^2=0` 

⇒`x=b^2/2`   or`   x=a^2/2` 

Hence, the roots of the equation are `b^2/2` and  `a^2/2`