+2669 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 + ___
+129850 3x^2 - 16x + 17 = 0
Product of the roots = 17/3 = ab
(ab)^2 = a^2*b^2 = 289 / 9
2ab = 34/3
Sum of the roots = 16/3 = a + b square both sides
a^2 + 2ab + b^2 = 256 / 9
a^2 + (34/3) + b^2 = 256 / 9
a^2 + b^2 = 256 / 9 - 34 /3 = 154 / 9
Quadratic is
x^2 - (154/9)x + 289 / 9
