How many roots of the equation $z^4+8z^3+3z^2+8z+3=0$ lie in the right half plane?
The hint is to apply the argument principle. I am not sure how that will go. I can take $f(z)=z^4+8z^3+3z^2+8z+3$, so that for any closed curve $C$, $$\int_C\frac{f'(z)}{f(z)}dz=2\pi i(N-P)$$ where $N$ and $P$ denote respectively the number of zeros and poles of $f(z)$ inside the contour $C$. But here we are looking at the right half plane. I can't see how to apply the result from the argument principle.
http://math.stackexchange.com/questions/31651/roots-of-fz-z48z33z28z3-0-in-the-right-half-plane?rq=1
– Riemann1337 Oct 26 '13 at 02:33