With the roots 2, and 6 + i, find the simplest polynomial expression

Question

How would you solve this?

Answer 1

If 6+i is a root, then so is 6-i.  Here are some tips to get you started.

 

First, your zeros are 2, 6+i and 6-i.  So you factors are (x-2)[x-(6+i)][x-(6-i)]

 

Start by multiplying those two i pieces.  If you do that correctly, i will disappear, and you'll get an unfactorable quadratic.  Next, work in the (x-2), and you'll have your simple polynomial.