Chapter 14.11, Problem 4MP

Use Liouville’s theorem (Problem 3 ) to prove the fundamental theorem of algebra (see Problem 7.44). Hint: Let $P(z)$ be a polynomial of degree $\ge 1;$ then $f(z)=$ $1/P(z)$ is a bounded analytic function in a region not containing any zeros of $P(z)$ Disprove the assumption that $P(z)$ has no zeros anywhere.