@prefix psr: . @prefix skos: . @prefix dc: . @prefix xsd: . psr:-W96QGKZX-0 skos:prefLabel "elementary algebra"@en, "algèbre élémentaire"@fr ; a skos:Concept ; skos:narrower psr:-M35LK8SS-5 . psr: a skos:ConceptScheme . psr:-M35LK8SS-5 skos:altLabel "root of a function"@en, "point d'annulation d'une fonction"@fr ; skos:broader psr:-W96QGKZX-0 ; skos:definition """En mathématiques, un zéro ou point d'annulation d'une fonction est une valeur en laquelle cette fonction s'annule. Autrement dit, il s'agit d'un antécédent de la valeur zéro.
En particulier en analyse réelle, les zéros d'une fonction d'une variable correspondent aux abscisses des points d'intersection de sa courbe avec l'axe des abscisses.
La détermination des zéros d'une fonction f revient à résoudre l'équation f(x)=0.
(Wikipedia, L'Encylopédie Libre, https://fr.wikipedia.org/wiki/Z%C3%A9ro_d%27une_fonction)"""@fr, """In mathematics, a zero (also sometimes called a root) of a real-, complex-, or generally vector-valued function

{\\\\displaystyle f}

, is a member

{\\\\displaystyle x}

of the domain of

{\\\\displaystyle f}

such that

{\\\\displaystyle f(x)}

vanishes at

{\\\\displaystyle x}

; that is, the function

{\\\\displaystyle f}

attains the value of 0 at

{\\\\displaystyle x}

, or equivalently,

{\\\\displaystyle x}

is a solution to the equation

{\\\\displaystyle f(x)=0}

. A "zero" of a function is thus an input value that produces an output of 0. A root of a polynomial is a zero of the corresponding 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

{\\\\displaystyle f}

of degree two, defined by

{\\\\displaystyle f(x)=x^{2}-5x+6}

has the two roots (or zeros) that are 2 and 3.

{\\\\displaystyle f(2)=2^{2}-5\\ imes 2+6=0{\\ ext{ and }}f(3)=3^{2}-5\\ imes 3+6=0.}

If the function maps real numbers to real numbers, then its zeros are the

{\\\\displaystyle x}

-coordinates of the points where its graph meets the x-axis. An alternative name for such a point

{\\\\displaystyle (x,0)}

in this context is an ${\\\\displaystyle x}$ -intercept.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Zero_of_a_function)"""@en ; skos:prefLabel "zero of a function"@en, "zéro d'une fonction"@fr ; a skos:Concept ; skos:inScheme psr: ; skos:exactMatch , ; dc:modified "2024-10-18"^^xsd:date .