Let a and b be the roots of the quadratic x^2 - 5x + 3 = 2x^2 - 7x + 11. Find the quadratic whose roots are a^4 and b^4.
+128474 Rearrange the given equation as
x^2 - 2x + 8 = 0
(x - 4) ( x + 2) = 0
The roots are 4 , -2 = a , b
4^4 = 256 = a^4
(-2)^4 = 16 = b^4
The sum of these roots = -b in the new quadratic = -272
The product of these roots = c in the new quadratic = 4096
The new quadratic = x^2 - 272x + 4096
