Find the number of polynomial zeros of $z^4-7z^3-2z^2+z-3=0$. 
Find the number of solutions of $$z^4-7z^3-2z^2+z-3=0$$ inside the unit disc.

The Rouche theorem fails obviously. Is there any other method that can help?
I have known the answer by Matlab, but I have to prove it by complex analysis.
Thanks!

Note that $|z^4-2z^2+z-3|<7$ if $|z|=1$. The triangle inequality only says "$\leq$" but equality can only occur if $z^4$, $-2z^2$, $z$ and $-3$ all have the same argument. So it suffices to check $z=-1$.
