Number of zeros with positive real part
How many zeros does the polynomial $z^4 + 3z^2 + z + 1$ have in the right
half-plane?
This question is from a previous exam and I am not sure how to solve it.
The other questions in this section are applications of Rouché's theorem.
I tried to change this to a question about the unit disc, using the map $z
\mapsto \frac{z-1}{z+1}$, which (I think) maps $\{z : \mathfrak{Re}(z) >
0\}$ bijectively to the unit disc and turns rational functions into
rational functions. In this way I could reduce to counting the zeros of
$4z^4 + 2z^3 + 6z^2 - 2z + 6$ on the unit disc. This looks like a standard
Rouché's theorem problem, but I don't see how to do it.
Is it possible that there is a better solution?
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