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Root (mathematics)

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	Topics Root (mathematics) Topic Home In mathematicsMathematics Mathematics is the discipline that deals with concepts such as quantity, structure, space and change.... , a root (or a zero) of a complex-valued functionFunction (mathematics) In mathematics, a function relates each of its inputs to exactly one output.... is a member of the domainDomain (mathematics) In mathematics, a domain of a k-place relation L ? X1 × × X'k is one of the sets X'j,... 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 numberReal number Overview In mathematics, the set of real numbers, denoted R, is the set of all rational numbers and irrational numbers.... s to real numbers, its zeros are the points where its graph meets the x-axis. In this situation, a root can be called an x-intercept. The word root can also refer to a number in the form (which is the root of the polynomial ) such as the square rootSquare root In mathematics, a square root of a number x is a number whose square is x.... or other roots. A substantial amount of mathematics was developed in order to find rootsRoot-finding algorithm A root-finding algorithm is a numerical method, or algorithm, for finding a value x such that f = 0, for a given fun... of various functions, especially polynomialPolynomial In mathematics, a polynomial is an expression in which a finite number of constants and variables are combined using only ad... s. One wide-ranging concept, complex numberComplex number In mathematics, a complex number is a number of the form ... s, was developed to handle the roots of quadraticQuadratic equation In mathematics, a quadratic equation is a polynomial equation of the second degree.... or cubic equationCubic equation Overview In mathematics, a cubic equation is a polynomial equation in which the highest occurring power of the unknown is the third p... s with negative discriminantDiscriminant In mathematics, a discriminant is an expression that discriminates qualities of algebraic structures.... (that is, those leading to expressions involving the square root of negative numbersNegative and non-negative numbers A negative number is a number that is less than zero, such as −3.... ). All real polynomials of odd degreeDegree (mathematics) In mathematics, there are several meanings of degree depending on the subject. ... have a real number as a root. Many real polynomials of even degree do not have a real root, but the fundamental theorem of algebraFundamental theorem of algebra In mathematics, the fundamental theorem of algebra states that every complex polynomial in one variable and of degree has ... states that every polynomial of degree has complex roots, counted with their multiplicitiesMultiplicity In mathematics, the multiplicity of a member of a multiset is how many memberships in the multiset it has.... . The non-real roots of polynomials with real coefficients come in conjugateComplex conjugate In mathematics, the complex conjugate... pairs. One of the most important unsolved problems in mathematicsUnsolved problems in mathematics This article lists some currently unsolved problems in mathematics.... concerns the location of the roots of the Riemann zeta functionRiemann zeta function In mathematics, the Riemann zeta function, named after Bernhard Riemann, is a function of significant importance in number t... . See also zero (complex analysis)Zero (complex analysis) In complex analysis, a zero of a holomorphic function f is a complex number a such that f = 0. ... pole (complex analysis)Pole (complex analysis) In complex analysis, a pole of a holomorphic function is a certain type of simple singularity that behaves like the singular...