# How do you find all the real and complex roots of #p(x) = x^5 + 4x^4 + 6x^3 + 4x^2 + 5x#?

##### 1 Answer

Jan 11, 2016

The zeros are

#### Explanation:

First separate out the common factor

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

Note that

Next, let

This is called a Tschirnhaus transformation. This kind of simple Tschirnhaus transformation can be used normally to eliminate the

Then

So

This has zeros when

That is when

If

If