Solve for x:
4x2 - 2(a2 + b2)x + a2b2 = 0
4x2 – 2 (a2 + b2) x + a2b2 = 0
⇒ 4x2 – 2a2x –2b2x + a2b2 = 0
⇒ 2x (2x –a2) – b2 (2x –a2) = 0
⇒ (2x – a2) (2x – b2) = 0
⇒ 2x – a2 = 0 or 2x – b2 = 0
⇒ 2x = a2 or 2x = b2
Hence, the roots of the quadratic equation are 
and 
.