Let a and b be the roots of the quadratic x^2 - 5x + 3 = -2x^2 + 11x - 14. Find the quadratic whose roots are a^2 and b^2. x^2 + ___x + ___
Rearrange as
3x^2 - 16x + 17 = 0
ab = 17/3 → 2ab = 34/3
a + b = 16/3 square both sides
a^2 + 2ab + b^2 = 256/9
a^2 + 34/3 + b^2 = 256/9
a^2 + b^2 = 154/9
ab = 17/3
(ab)^2 = 289/9
a^2 * b^2 = 289 / 9
The polynomial is
x^2 - (154/9)x + 289 / 9
+729 
