AMC 12 2001 Problem 23

A polynomial of degree four with leading coefficient 1 and integer coefficients has two real zeros, both of which are integers. Which of the following can also be a zero of the polynomial?

$\text{(A) }\frac {1 + i \sqrt {11}}{2} \text{(B) }\frac {1 + i}{2} \text{(C) }\frac {1}{2} + i \text{(D) }1 + \frac {i}{2} \text{(E) }\frac {1 + i \sqrt {13}}{2}$