Question

Find a polynomial f(x) of degree 3 with real coefficients and the following zeros. 2,-3+i

Answer 1

Complex roots are in pairs for a cubic and u can find the polynomial here

http://www.wolframalpha.com/input/?i=%28x-2%29%28x-%28-3%2Bi%29%29%29%28x-%28-3-i%29%29

Answer 2

what you should know is that if \[-3+i\] is a root, then so is it's conjugate \[-3-i\]

Answer 3

then write in factored form
\[(x-2)(x-(-3+i))(x-(-3-i))\] and then multiply out, which is not as hard as it seems

Answer 4

second product is actually simple.

\[(a+bi)(a-bi)=a^2+b^2\]
so you get
\[(x-2)(x^2+6x+10)\]

Answer 5

x^3+4x^2-2x-20 is what I came up with

Answer 6

Both are here:

http://www.wolframalpha.com/input/?i=%28x-2%29%28x-%28-3%2Bi%29%29%29%28x-%28-3-i%29%29

Answer 7

One is factored, other not...

Answer 8

(x−2)(x 2 +6x+10) ?