# Polynomial Equations and Maximum Coefficients

If $\alpha$ is a root of a polynomial equation $P(x) = 0$, then $P(\alpha) = 0$, and if $M$ is the maximum coefficient value of $|a_{n}|, |a_{n-1}|, |a_{n-2}|, \cdots ,|a_2|, |a_1|$ then $nM \ge |a_{n}| + |a_{n-1}| + |a_{n-2}| + \cdots + |a_2| + |a_1|$. […]