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

Algebra ->  Polynomials-and-rational-expressions -> 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      Log On


   

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) About Me  (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 -sqrt%287%29 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, sqrt%287%29, -sqrt%287%29, 7+4i, 7-4i