Find a fourth-degree polynomial with integer coefficients that has zeros 4i and −1, with −1 a zero of multiplicity 2. (Use x for the variable.)

Question

can somebody help me do this?

Answer 1

If 4i is a zero, then -4i must also be a zero, since complex zeros come in conjugate pairs.

a possible polynomial is
f(x) = (x-4i)(x+4i)(x+1)^2

a general solution would be
f(x) = a(x-4i)(x+4i)(x+1)^2 , where a is a non-zero integer.

If necessary, your can expand this.