finding the sum of the absolute values for the roots How to find the sum of the absolute values for the roots of this equation:
$$x^4-4x^3-4x^2+16x-8=0$$

Notice that
$$\begin{align}x^4-4x^3-4x^2+16x-8 &= (x-1)^4 - 10(x-1)^2 + 1 \\
&= ((x-1)^2-5)^2-24 \end{align}$$
so you can actually calculate the roots explicitly and sum their absolute values.
