In mathematics, a root (or a zero) of a function f is an element x in the domain of f such that Wikibooks Wikiversity has more about this subject: School of Mathematics Wikiquote has a collection of quotations related to: Mathematics Look up Mathematics on Wiktionary, the free dictionary Wikimedia Commons has more media related to: Mathematics Bogomolny, Alexander: Interactive Mathematics Miscellany and Puzzles. ... In mathematics, a function is a relation, such that each element of a set (the domain) is associated with a unique element of another (possibly the same) set (the codomain, not to be confused with the range). ... In mathematics, the domain of a function is the set of all input values to the function. ...

f(x) = 0.

For an important special case see zero (complex analysis). In complex analysis, a zero of a holomorphic function f is a complex number a such that f(a) = 0. ...

Consider the equation:

Now 3 is called a root of f, because f(3) = 3² - (6 x 3) + 9 = 0.

If the function is mapping from real numbers to real numbers, its zeros are essentially where its graph hits the x-axis. In this situation, the root can be called a x-intercept. In mathematics, the real numbers are intuitively defined as numbers that are in one-to-one correspondence with the points on an infinite line—the number line. ... In mathematics, the real numbers are intuitively defined as numbers that are in one-to-one correspondence with the points on an infinite line—the number line. ... Cartesian means relating to the French mathematician and philosopher Descartes, who, among other things, worked to merge algebra and Euclidean geometry. ...

The word root can also refer to a number in the form x^1/a, such as the square root or other roots. In mathematics, the principal square root of a non-negative real number is denoted and represents the non-negative real number whose square (the result of multiplying the number by itself) is . ... In mathematics, the nth root or radical of the non-negative real number a, written as , is the unique non-negative real number b such that bn = a. ...

A substantial amount of mathematics was developed in order to find roots of various functions, especially polynomials. One wide-ranging concept, complex numbers, was developed to handle the roots of quadratic equations with negative discriminant (that is, those leading to expressions involving the square root of negative numbers). Wikibooks Wikiversity has more about this subject: School of Mathematics Wikiquote has a collection of quotations related to: Mathematics Look up Mathematics on Wiktionary, the free dictionary Wikimedia Commons has more media related to: Mathematics Bogomolny, Alexander: Interactive Mathematics Miscellany and Puzzles. ... A root-finding algorithm is a numerical method or algorithm for finding a value x such that f(x) = 0, for a given function f. ... In mathematics, polynomial functions, or polynomials, are an important class of simple and smooth functions. ... In mathematics, the complex numbers are an extension of the real numbers by the inclusion of the imaginary unit i, satisfying . ... Graph of a quadratic function: y = x2 - x - 2 = (x+1)(x-2) The x-coordinates of the points where the graph crosses the x-axis, x = -1 and x = 2, are the roots of the quadratic equation: x2 - x - 2 = 0. ... In mathematics, a polynomial P(T) has a discriminant, which is a polynomial function of its coefficients, and discriminates the case of a multiple root (for which the graph of P(x) would touch the x-axis). ... A negative number is a number that is less than zero, such as −3. ...

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 n has n complex roots, counted with their multiplicities. The non-real roots of real polynomials come in conjugate pairs. In mathematics, the real numbers are intuitively defined as numbers that are in one-to-one correspondence with the points on an infinite line—the number line. ... In mathematics, polynomial functions, or polynomials, are an important class of simple and smooth functions. ... In mathematics, the real numbers are intuitively defined as numbers that are in one-to-one correspondence with the points on an infinite line—the number line. ... In mathematics, the fundamental theorem of algebra states that every complex polynomial of degree n has exactly n roots (zeroes), counted with multiplicity. ... In mathematics, polynomial functions, or polynomials, are an important class of simple and smooth functions. ... This article is about the term degree as used in mathematics. ... In mathematics, the complex numbers are an extension of the real numbers by the inclusion of the imaginary unit i, satisfying . ... This article is about the mathematical term; Multiplicity is also the title of a 1996 film. ...

One of the most important unsolved problems in mathematics concerns the location of the roots of the Riemann zeta function. In mathematics, the Riemann zeta function, named after Bernhard Riemann, is a function of paramount importance in number theory, because of its relation to the distribution of prime numbers. ...

Compare with the concept of a pole.