Zero of a function
A graph of the function cos(x) on the domain ![\scriptstyle{[-2\pi,2\pi]}](http://assets.wn.com/wiki/en/4/5b/c9821938564ef43a95df5-b7e91f.png)
, with x-intercepts indicated in red. The function has zeroes where x is 
, 
, 
and 
.
In mathematics, a zero, also sometimes called a root, of a real-, complex- or generally vector-valued function f is a member x of the domain of f such that f(x) vanishes at x; that is, x is a solution of the equation
In other words, a "zero" of a function is an input value that produces an output of zero (0).
A root of a polynomial is a zero of the associated polynomial function.
The fundamental theorem of algebra shows that any non-zero polynomial has a number of roots at most equal to its degree and that the number of roots and the degree are equal when one considers the complex roots (or more generally the roots in an algebraically closed extension) counted with their multiplicities. For example, the polynomial f of degree two, defined by
has the two roots 2 and 3, since
If the function maps real numbers to real numbers, its zeroes are the x-coordinates of the points where its graph meets the x-axis. An alternative name for such a point (x,0) in this context is an x-intercept.
