A problem in my topology course asks to show that there exists a large enough $R$ such that $f(x)=z_n x^n + \dots + z_0$ has no roots on $ \mid z \mid =R$.
I am not sure how to approach this problem or where to begin looking, when I search online I am just directed to polynomials whose roots lie on the unit circle.
Also, I have not seen much complex analysis so hopefully it will not play a major role.
Thanks for any pointers in the right direction.