Root of a Polynomial

algebra

Definition

Root of a Polynomial

Let $F$ be a field and $p\in F[x]$ a polynomial. An element $\alpha \in F$ is a root (or zero) of $p$ if

$$p(\alpha )=0.$$

By the Factor Theorem, $\alpha$ is a root of $p$ iff $(x-\alpha )$ divides $p$ in $F[x]$.