Find a polynomial function f(x) of least degree having only real coefficients with zeros of 0, 2i, and 4+i

Answer 1

x=4+i

x-4 =i

(x-4)^2 =-1

x^2 -8x +16 = -1

x^2-8x+17 =0

x=i

x^2 =-1

X^2+1 = 0

f(x) = x(x^2+1)(x^2-8x+17), a 5th degree polynomial with one real zero and four imaginary zeros