# How do you find a third degree polynomial given roots #5# and #2i#?

##### 1 Answer

Nov 7, 2016

Please see the explanation section below.

#### Explanation:

For a third degree polynomial, we need 3 linear factors.

Since

If we want a polynomial with real coeficients, then the complex conjugate of

One polynomial with real coefficients that meets the requirements is

# = x^3-5x^2+4x-20#

Any constant multiple of this also meets the requirements.

For example