Quartic Polynomial with rational coefficients has the roots...

Question

A quartic polynomial equation with rational coefficients has the roots 3 + (square root of 6), 5-4i. Find all additional roots.

Answer 1

In order to have rational coefficients, 3 - √6 must also be a root.  In order to have real coefficients, 5 - 4i must also be a root.  The 4 roots are

 

3 + √6

3 - √6

5 - 4i

5 + 4i