How do you find all the real and complex roots of #p(x) = x^5 + 4x^4 + 6x^3 + 4x^2 + 5x#?
The zeros are
First separate out the common factor
#p(x) = x(x^4+4x^3+6x^2+4x+5)#
This is called a Tschirnhaus transformation. This kind of simple Tschirnhaus transformation can be used normally to eliminate the
This has zeros when
That is when