Here is one of the comp questions I need to solve.
Find the smallest integer N such that the polynomial $p(z)=2z^5-9z+2012$ has a zero in the open disk of radius N centered at the origin. How many zeros does $P(z)$ have in this open disk?
So I started with the smallest integer 1 and ended up with the integer 4 where I chose $f(z)=2z^5-9z$ and $g(z)=2012$. Plugging the value N=4 gives me $|f(z)|>=2012$ and $|g(z)|=2012$ on $|z|=4$. From there I can not use Rouche's Theorem. My understanding is that to use Rouche's Theorem you have to have strict inequality hold. Since we are looking for the minimum integer, I do not think we can choose N=5 in this case.
Is there any other way than Rouche's Method? Or am I missing something?