Summary

Polynomial equation

Root of Polynomial

Let $p(x)$ be a polynomial of degree $n$ with complex coefficients. Then, $p(x)$ has at $n$ roots in the complex plane (counting the multiple roots)

Multiplicity of $z_0$

When $p(z)=(z-z_0{)}^{m}q(z)$ where $q(z)$ is a polynomial that does not have $z_0$ as a root. The multiplicity of $z_0$ is $m$.