Question

Suppose that a polynomial function of degree 4 with rational coefficients has -2, -6, -5-i as zeros. Find the other zero.

Answer 1

complex roots (zeros) occur in conjugate pairs __ if 7+4i is a zero, then 7-4i is also a zero


for the coefficients to be rational; any irrational zeros (sqrt(7)) must have a conjugate, so -sqrt(7) is also a zero