Find an nth degree polynomial with real coefficients satisfying the given conditions

Question

n+3; -4 and i are zeros; f(-3) = 60

Answer 1

I assume you meant to say n=3 (not n+3).

The complex conjugate of a complex zero must also be a zero, so your zeros are

-4

i

-i

f(x) = A(x + 4)(x - i)(x + i) = A(x + 4)(x² + 1)

f(-3) = 60

A(-3 + 4)[(-3)² + 1] = 60

10A = 60

A = 6

f(x) = 6(x + 4)(x² + 1)