If and are the roots of the equation x^2+p x+q=0 , then the value of ^2( + )+p ( + ) ( + )+q ^2( + ) is

Step-by-step solution

Given that, and are the roots of the equation x^2+p x+q=0 + =-p and =q Now, ( + )= + 1- aligned & = -p 1-q = p q-1 & ( + )= 1+ ^2( + ) & ( + )= 1+ p^2 (q-1)^2 & ( + )= 1 1+ p^2 (q-1)^2 & ^2( + )+p ( + ) ( + ) & = ^2( + ) [ ^2( + )+p ( + )+q ] & = 1 1+ p^2 (q-1)^2 [ p^2 (q-1)^2+ p^2 q-1 +q ] & = (q-1)^2 (q-1)^2+p^2 [ p^2+p^2(q-1)+q(q-1)^2 (q-1)^2 ] aligned