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

Question

N=4 , -2, -1/2 and I are zeros; f(1) =18

Answer 1

I will assume that you meant to say the zeros are -2,-1/2, i (not I)

The complex conjugate of a complex zero must also be a zero, so you will have 4 zeros:

-2

-1/2

i

-i

f(x) = A(x + 2)(x + 1/2)(x - i)(x + i) = A(x + 2)(x + 1/2)(x² + 1)

18 = A(1 + 2)(1 + 1/2)(1² + 1)

18 = A(3)(3/2)(2)

18 = 9A

A = 2

f(x) = 2(x + 2)(x + 1/2)(x² + 1)