discriminant of a polynomial

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• 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 of an algebraic number field — A fundamental domain of the ring of integers of the field K obtained from Q by adjoining a root of x3 − x2 − 2x + 1. This fundamental domain sits inside K ⊗QR. The discriminant of K is 49 = 72.… …   Wikipedia

• discriminant — 1. noun An expression that gives information about the roots of a polynomial; for example, the expression D = b 4ac determines whether the roots of the quadratic equation ax + bx + c = 0 are real and distinct (D > 0), real and …   Wiktionary

• List of polynomial topics — This is a list of polynomial topics, by Wikipedia page. See also trigonometric polynomial, list of algebraic geometry topics.Basics*Polynomial *Coefficient *Monomial *Polynomial long division *Polynomial factorization *Rational function *Partial… …   Wikipedia

• Symmetric polynomial — This article is about individual symmetric polynomials. For the ring of symmetric polynomials, see ring of symmetric functions. In mathematics, a symmetric polynomial is a polynomial P(X1, X2, …, Xn) in n variables, such that if any of the… …   Wikipedia

• Separable polynomial — In mathematics, two slightly different notions of separable polynomial are used, by different authors. According to the most common one, a polynomial P(X) over a given field K is separable if all its roots are distinct in an algebraic closure of… …   Wikipedia

• Algebraic number field — In mathematics, an algebraic number field (or simply number field) F is a finite (and hence algebraic) field extension of the field of rational numbers Q. Thus F is a field that contains Q and has finite dimension when considered as a vector… …   Wikipedia

• Ulam spiral — The Ulam spiral to 150 iterations. Red dots represent prime numbers; blue dots represent composite numbers, with the size of the dot indicating the degree of compositeness. The Ulam spiral, or prime spiral (in other languages also called the Ulam …   Wikipedia

• Multiplicity (mathematics) — In mathematics, the multiplicity of a member of a multiset is the number of times it appears in the multiset. For example, the number of times a given polynomial equation has a root at a given point. The notion of multiplicity is important to be… …   Wikipedia

• Delta (letter) — Greek alphabet Αα Alpha Νν Nu Ββ Beta …   Wikipedia