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}