Question

Write the simplest polynomial function with the given zeros: 2-i, square root of 3, and 2.
I get the (x+2-i)(x+2+i)(x+root3)(x-root3)(x-2). but where do I go from here?

Answer 1

if \(2-i\) is a zero then \(x-(2-i)\) will be a factor

Answer 2

so you should get

\[(x-(2-i))(x-(2+i))(x-\sqrt{3})(x+\sqrt{3})(x-2)\]

Answer 3

expanding gives you
http://www.wolframalpha.com/input/?i=EXPAND++%28x-%282-i%29%29%28x-%282%2Bi%29%29%28x-%5Csqrt%7B3%7D%29%28x%2B%5Csqrt%7B3%7D%29%28x-2%29