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?

Answer Choices
A. \dfrac{1+i \sqrt{11}}{2}
B. \dfrac{1+i}{2}
C. \dfrac{1}{2}+i
D. 1+\dfrac{i}{2}
E. \dfrac{1+i \sqrt{13}}{2}