# How do you find all roots #x^4 - 4x^3 + 6x^2 - 4x + 5# given one root 2 -i?

##### 1 Answer

Aug 14, 2016

This quartic has zeros

#### Explanation:

Since the coefficients of

So if

Then:

#(x-2+i)(x-2-i) = (x-2)^2-i^2 = x^2-4x+5#

We find:

#x^4-4x^3+6x^2-4x+5 = (x^2-4x+5)(x^2+1)#

The remaining zeros, which are those of