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2001 AMC 12 Question 23

AMC12 · 2001 AMC 12

Question 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?
  1. $\dfrac{1 + i\sqrt{11}}{2}$
  2. $\dfrac{1 + i}{2}$
  3. $\dfrac{1}{2} + i$
  4. $1 + \dfrac{i}{2}$
  5. $\dfrac{1 + i\sqrt{13}}{2}$