There are integers and such that the polynomial has as a root. What is
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Since is a root and all the coefficients are integers, the conjugate must also be a root. By Vieta's, the roots sum to , so the last root must be . Hence the polynomial must be:
and so . This yields a final answer of .
Alternate Solution:
Suppose was the desired polynomial. Then . We found the roots to be , , and , so we could calculate:
and so , which leads to the same as before.
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