SOLUTION: I am working on this questions and need help. Suppose that a polynomial function of degree 5 with rational coefficients has 3, square root of 7, 7+4i as zeros. Find the other ze

Question 166407: I am working on this questions and need help.
Suppose that a polynomial function of degree 5 with rational coefficients has 3, square root of 7, 7+4i as zeros. Find the other zeros.
Any help you can provide me with is greatly appreciated.
Thanks in Advance!
Answer by Personal Trainer DC(4) (Show Source): You can put this solution on YOUR website!
Since the polynomial is degree 5, it has 5 zeros. Also its coefficients are all rational so its zeros must form rational coefficients. The square root of 7 (or any non-square) is irrational so we must take to be a zero as well. Also, 7+4i is imaginary and not rational so we must take its conjugate, 7-4i, to form a rational coefficient.
So, your zeros are: 3, , , 7+4i, 7-4i
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