- Root (mathematics)
:"This article is about the zeros of a function, which should not be confused with the value at zero. You may also want information on the
Nth root s of numbers instead."In
mathematics , a root (or a zero) of a complex-valued function is a member of the domain of such that vanishes at , that is,:
In other words, a "root" of a function is a value for that produces a result of zero ("0"). For example, consider the function defined by the following formula::This function has a root at 3 because .
If the function is mapping from
real number s to real numbers, its zeros are the points where its graph meets the "x"-axis. The x-value of such a point is called x-intercept. Therefore in this situation a root can be called an "x"-intercept.The word root can also refer to the
nth root of a number, a, as in .Thesquare root of a number,a, is .A substantial amount of mathematics was developed in order to find roots of various functions, especially
polynomial s. One wide-ranging concept,complex number s, was developed to handle the roots of quadratic orcubic equation s with negativediscriminant (that is, those leading to expressions involving the square root of negative numbers).All real polynomials of odd degree have a real number as a root. Many real polynomials of even degree do not have a real root, but the
fundamental theorem of algebra states that every polynomial of degree has complex roots, counted with their multiplicities. The non-real roots of polynomials with real coefficients come in conjugate pairs.Vieta's formulas relate the coefficients of a polynomial to sums and products of its roots.One of the most important
unsolved problems in mathematics concerns the location of the roots of theRiemann zeta function .ee also
*
zero (complex analysis)
*pole (complex analysis)
* other roots
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