Let r and s be the roots of 3x^2 + 4x + 12 = 2x^2 - 7x + 1. Find r^2 + s^2.
3x^2 + 4x + 12 = 2x^2 - 7x + 1 rearrange as
x^2 + 11x + 11 = 0
r + s = -11 square both sides
r^2 + 2rs + s^2 =121
And rs = 11 so ..... 2rs = 22
So
r^2 + 22 + s^2 = 121
r^2 + s^2 + 22 = 121
r^2 + s^2 = 99
