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- Discriminant abstract "In algebra, the discriminant of a polynomial is a function of its coefficients, typically denoted by a capital 'D' or the capital Greek letter Delta (Δ). It gives information about the nature of its roots. For example, the discriminant of the quadratic polynomial isHere for real a, b and c, if Δ > 0, the polynomial has two real roots, if Δ = 0, the polynomial has one real double root, and if Δ < 0, the polynomial has no real roots. The discriminant of the cubic polynomial isFor higher degrees, the discriminant is always a polynomial function of the coefficients. It becomes significantly longer for the higher degrees. The discriminant of a general quartic has 16 terms, that of a quintic has 59 terms, that of a 6th degree polynomial has 246 terms,and the number of terms increases exponentially with the degree.[citation needed]A polynomial has a multiple root (i.e. a root with multiplicity greater than one) in the complex numbers if and only if its discriminant is zero. The concept also applies if the polynomial has coefficients in a field which is not contained in the complex numbers. In this case, the discriminant vanishes if and only if the polynomial has a multiple root in its splitting field.As the discriminant is a polynomial function of the coefficients, it is defined as soon as the coefficients belong to an integral domain R and, in this case, the discriminant is in R. In particular, the discriminant of a polynomial with integer coefficients is always an integer. This property is widely used in number theory.The term "discriminant" was coined in 1851 by the British mathematician James Joseph Sylvester.".
- Discriminant wikiPageExternalLink PolynomialDiscriminant.html.
- Discriminant wikiPageExternalLink Discriminant.html.
- Discriminant wikiPageID "55607".
- Discriminant wikiPageRevisionID "602645117".
- Discriminant hasPhotoCollection Discriminant.
- Discriminant subject Category:Algebraic_number_theory.
- Discriminant subject Category:Conic_sections.
- Discriminant subject Category:Determinants.
- Discriminant subject Category:Polynomials.
- Discriminant subject Category:Quadratic_forms.
- Discriminant type Abstraction100002137.
- Discriminant type Attribute100024264.
- Discriminant type Cognition100023271.
- Discriminant type CognitiveFactor105686481.
- Discriminant type ConicSection113872975.
- Discriminant type ConicSections.
- Discriminant type Determinant105692419.
- Discriminant type Determinants.
- Discriminant type Figure113862780.
- Discriminant type Form106290637.
- Discriminant type Function113783816.
- Discriminant type LanguageUnit106284225.
- Discriminant type MathematicalRelation113783581.
- Discriminant type Part113809207.
- Discriminant type PlaneFigure113863186.
- Discriminant type Polynomial105861855.
- Discriminant type Polynomials.
- Discriminant type PsychologicalFeature100023100.
- Discriminant type QuadraticForms.
- Discriminant type Relation100031921.
- Discriminant type Shape100027807.
- Discriminant type Word106286395.
- Discriminant comment "In algebra, the discriminant of a polynomial is a function of its coefficients, typically denoted by a capital 'D' or the capital Greek letter Delta (Δ). It gives information about the nature of its roots. For example, the discriminant of the quadratic polynomial isHere for real a, b and c, if Δ > 0, the polynomial has two real roots, if Δ = 0, the polynomial has one real double root, and if Δ < 0, the polynomial has no real roots.".
- Discriminant label "Discriminant".
- Discriminant label "Discriminant".
- Discriminant label "Discriminant".
- Discriminant label "Discriminante".
- Discriminant label "Discriminante".
- Discriminant label "Diskriminante".
- Discriminant label "Wyróżnik".
- Discriminant label "Дискриминант".
- Discriminant label "مميز".
- Discriminant label "判别式".
- Discriminant sameAs Diskriminant.
- Discriminant sameAs Diskriminante.
- Discriminant sameAs Discriminante.
- Discriminant sameAs Discriminant.
- Discriminant sameAs Discriminante.
- Discriminant sameAs 판별식.
- Discriminant sameAs Discriminant.
- Discriminant sameAs Wyróżnik.
- Discriminant sameAs m.0fg1z.
- Discriminant sameAs Q192487.
- Discriminant sameAs Q192487.
- Discriminant sameAs Discriminant.
- Discriminant wasDerivedFrom Discriminant?oldid=602645117.
- Discriminant isPrimaryTopicOf Discriminant.