I need help finding a polynomial equation of lowest degree, having integer coefficients and the following...?

Question

As some of its ZEROS....{4,-1,i}

I understand that (x-4) and (x+1) will be a factor but what about i? I am so confused. Please help!! Thank you in advance!

Answer 1

x^3 - (3+i)x^2 + (3i-4)x + 4i=0

Answer 2

If the polynomial has integer coefficients and i
is a root, so is -i. So your polynomial
is (x-4)(x+1)(x+ i)(x-i) = (x-4)(x+1)(x²+1), of degree 4.