Find an nth-degree polynomial function with real coefficients satisfying the given conditions. n = 3; 2 and 4 i are zeros; f (-1) = -51

Answer 1

a(x-2)(x-4i)(x+4i)

= a(x-2)(x^2 +16)

plug in (-1,-51) to solve for a

-51 = a(-3)(17) = -51a

a = 1

the 3 degree polynomial is

x^3 -2x^2 +16x -32