# discriminant

discriminant
discriminantal /dis krim'euh nan"tl/, adj.
/di skrim"euh neuhnt/, n. Math.
a relatively simple expression that determines some of the properties, as the nature of the roots, of a given equation or function.
[1830-40; < L discriminant- (s. of discriminans) separating, prp. of discriminare to divide up, separate, v. deriv. of discrimen, s. discrimin- separating line, distinction, equiv. to discri-, var. s. of discernere (see DISCERN) + -men n. suffix; see -ANT]

* * *

in mathematics, a parameter of an object or system calculated as an aid to its classification or solution. In the case of a quadratic equation ax2 + bx + c = 0, the discriminant is b2 − 4ac; for a cubic equation x3 + ax2 + bx + c = 0, the discriminant is a2b2 + 18abc − 4b3 − 4a3c − 27c2. The roots of a quadratic or cubic equation with real coefficients are real and distinct if the discriminant is positive, are real with at least two equal if the discriminant is zero, and include a conjugate pair of complex roots if the discriminant is negative. A discriminant can be found for the general quadratic, or conic, equation ax2 + bxy + cy2 + dx + ey + f = 0; it indicates whether the conic represented is an ellipse, a hyperbola, or a parabola.

Discriminants also are defined for elliptic curves, finite field extensions, quadratic forms, and other mathematical entities. The discriminants of differential equations (differential equation) are algebraic equations that reveal information about the families of solutions of the original equations.

* * *

Universalium. 2010.

Поможем решить контрольную работу

### Look at other dictionaries:

• discriminant — discriminant, ante [ diskriminɑ̃, ɑ̃t ] adj. et n. m. • 1877; lat. discriminare, de discrimen « point de séparation » 1 ♦ Didact. Qui établit une séparation, une discrimination. « Nous n avons plus aujourd hui la barricade discriminante » (Péguy) …   Encyclopédie Universelle

• discriminant — DISCRIMINÁNT, Ă, discriminanţi, te, adj., s.m. 1. adj. (Rar) Discriminatoriu. 2. s.m. Expresie matematică formată din coeficienţii unei ecuaţii de gradul doi. – Din fr. discriminant. Trimis de LauraGellner, 16.06.2004. Sursa: DEX 98 ﻿… …   Dicționar Român

• discriminant — discriminant, ante (entrée créée par le supplément) (di skri mi nan, nan t ) adj. Terme didactique. Qui établit une séparation entre deux termes.    S. m. Terme de mathématique. Si on différentie une forme à k variables, le résultant de ces k… …   Dictionnaire de la Langue Française d'Émile Littré

• Discriminant — Dis*crim i*nant, n. [L. discriminans, p. pr. of discriminare.] (Math.) The eliminant of the n partial differentials of any homogenous function of n variables. See {Eliminant}. [1913 Webster] …   The Collaborative International Dictionary of English

• discriminant — [dis krim′ənənt] n. Math. an expression whose value or sign is used to classify functions …   English World dictionary

• Discriminant — In algebra, the discriminant of a polynomial is an expression which gives information about the nature of the polynomial s roots. For example, the discriminant of the quadratic polynomial is Here, if Δ > 0, the polynomial has two real roots,… …   Wikipedia

• Discriminant — Incidence du signe du discriminant sur les racines de l équation du second degré à coefficients réels En mathématiques, le discriminant est une notion algébrique. Il est utilisé pour résoudre des équations du second degré. Il se généralise pour… …   Wikipédia en Français

• discriminant — diskriminantas statusas T sritis fizika atitikmenys: angl. discriminant vok. Diskriminant, m rus. дискриминант, m pranc. discriminant, m …   Fizikos terminų žodynas

• discriminant — dis•crim•i•nant [[t]dɪˈskrɪm ə nənt[/t]] n. math. a relatively simple mathematical expression that determines some of the properties, as the nature of the roots, of a given equation or function • Etymology: 1830–40; < L discrīminant , s. of… …   From formal English to slang

• Discriminant validity — describes the degree to which the operationalization is not similar to (diverges from) other operationalizations that it theoretically should not be similar to. Campbell and Fiske (1959) introduced the concept of discriminant validity within… …   Wikipedia