r and s are the roots of 3x^2 + 4x - 12 = 0. What is r^3 + s^3?
By Vieta
r + s = -4/3 square both sides
r^2 + 2rs + s^2 = 16/9 (1)
And
rs =-12/3 = -4
-rs = 4
2rs = -8 (2)
Sub (2) into (1)
r^2 + s^2 - 8 = 16/9
r^2 + s^2 = 88/9
r^3 + s^3 = (r + s) (r^2 - rs + s^2) = (-4/3) ( 88/9 + 4 ) = (-4/3) ( 124/9)= -496 / 27
