Definition:Root of Polynomial

Definition
Let $R$ be a commutative ring with unity.

Let $f \in R[x]$ be a polynomial over $R$.

A root in $R$ of $f$ is an element $x\in R$ for which $f \left({x}\right) = 0$, where $f(x)$ denotes the image of $f$ under the evaluation homomorphism at $x$.

Also known as
A root of a polynomial is also known as a zero.