Rouche's Theorem: Find Zeros of f(z)=z^9-2z^6+z^2-8z-2 Inside Unit Circle

[AcC]

Homework Statement

Find the number of zeros of the folowing polynomial lying inside the unit circle,
f(z)= z^9 - 2z^6 + z^2 - 8z - 2

The Attempt at a Solution

Rouche's Theorem says if f and g differentiable which contains a simple loop s and all points inside s.
if |f(z)-g(z)|<|f(z)| for all z=s(t)
then f and g have same zeros inside s.

which g(z) should I choose, -2z^6, or z^2 or -8z
how can I determine?

 

[micromass]

Try, -8z. In general, try the term with the highest coefficient...