Algebra College

Question

n=4;

i and 2i are zeros;

f(-1)=30

Answer 1

By conjugate zero theorem -i and -2i are zeros also; in factored form f(x) = a(x - i)(x + i)(x - 2i)(x + 2i) =

a(x² + 1)(x² + 4); now f(-1) = a(1 + 1)(1 + 4) = 10a = 30; a = 3.

f(x) = 3(x² + 1)(x² + 4) = 3x⁴ + 15x² + 12.