Definition:Root of Polynomial
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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.
- 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