= Root of a polynomial
= Roots of a polynomial
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= Polynomial root
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A root of a polynomial $f$ is a scalar $a$ satisfying $f(a)=0$ in the chosen <field> or <ring>. For $p(X)=(X+1)(X-2)^2$ over the <real numbers>, the distinct <roots of a polynomial> are $-1$ and $2$. The second has <multiplicity of a root> two, so there are three roots when counted with multiplicity.
The domain matters. $X^2+1$ has no real <polynomial root>, but has the two <complex number> roots $i,-i$. The <fundamental theorem of algebra> guarantees a <polynomial root> in the <complex numbers> for every nonconstant complex <polynomial>, and complete factorization counts its <degree of a polynomial> many roots with <multiplicity of a root>. It does not promise that those roots are real or that they have a simple expression.
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