Possible complex root
Source: 2001 AMC-12 #23
December 4, 2005
algebrapolynomialquadraticscomplex numbersAMC
Problem Statement
A polynomial of degree four with leading coefficient 1 and integer coefficients has two zeros, both of which are integers. Which of the following can also be a zero of the polynomial?
(A) \ \frac {1 \plus{} i \sqrt {11}}{2} \qquad (B) \ \frac {1 \plus{} i}{2} \qquad (C) \ \frac {1}{2} \plus{} i \qquad (D) \ 1 \plus{} \frac {i}{2} \qquad (E) \ \frac {1 \plus{} i \sqrt {13}}{2}