Zeros of a function

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Given a function $f(x)$, the zeros of a function are the values $x$ such that $f(x)=0$. For example, some zeroes of the Riemann zeta function are –2, –4, –6, –8, etc., and ${\frac {1}{2}}+(14.13472\ldots )i.$

A nonconstant polynomial has a number of zeros (with multiplicity) equal to its degree: this is the fundamental theorem of algebra. For example, $f(x)=x^{2}+1$ has two zeroes ($i$ and $-i$), $f(x)=x^{3}+1$ has three roots (–1, $\omega$ and $\omega ^{2}$, where $\omega$ is the complex cubic root of unity), $f(x)=x^{4}+1$ has four zeros, etc.