# Definition:Root of Polynomial

## Definition

Let $R$ be a commutative ring with unity.

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

A **root** in $R$ of $f$ is an element $x \in R$ for which $\map f x = 0$, where $\map f x$ 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**.

## Sources

- 1969: C.R.J. Clapham:
*Introduction to Abstract Algebra*... (previous) ... (next): Chapter $8$: Field Extensions: $\S 37$. Roots of Polynomials - 1981: Murray R. Spiegel:
*Theory and Problems of Complex Variables*(SI ed.) ... (previous) ... (next): $1$: Complex Numbers: Polynomial Equations