information is given about the polynomial f(x) whose coefficients are real numbers. find the real zeros of f:

Question

degree 4; zeros: i, 3+i

Answer 1

complex roots always come in conjugate pairs
so if i is a root so is -i, and if 3+i is a root, so is 3-i

so f(x) = (x^2+1)(x - (3+i))(x - (3-i)
= (x^2 + 1)((x^2 + 6x + 10)

There are no real zeros.

Answer 2

am sorry i wrote in incoreectly forgive me, it was suppose to say: information is given about the polynomial f(x) whose coefficients are real numbers. find the remaining zeros of f: degree 4; zeros: i, 3+i, sorry again and thank you for taking the time to explain to me and solve the problem, god bless you always:)