# Polynomial Equation and Maximum Coefficient

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 $$nM \ge |a_{n}| + |a_{n-1}| + |a_{n-2}| + \cdots + |a_2| + |a_1|$$. […]