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Cubic equation

In algebra, a cubic equation in one variable is an equation of the form a x 3 + b x 2 + c x + d = 0 {\displaystyle ax^{3}+bx^{2}+cx+d=0} in which a is not zero.

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Overview

History

Factorization

Depressed cubic

Discriminant and nature of the roots

Cardano's formula

General cubic formula

Trigonometric and hyperbolic solutions

Geometric solutions

Geometric interpretation of the roots

Galois group

Derivation of the roots

Applications

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Cubic equation

Nodes168
Edges167
Triples163
Avg. degree1.99
Density0.011905
Components1

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Cubic equation

Top relations

related to Further reading · 46
Cubic equation → Anglin, Basic, Cambridge University Press, Ch, Cubic Equations, Cubics, Dence, Dover, Edgar, Explicit, Flannery, ISBN, ISSN, Joachim, JSTOR, July, Lambek, Mathematical Association, Mathematical Gazette, Mathematics
related to history · 26
Cubic equation → AD, Archimedes, Archimedes's, Babylonian, Babylonians, BC, Chinese, Cubic, Diophantine, Diophantus, Egyptians, Greek, Greeks, Heath, Hippocrates, In, Indians, Liu Hui, Mathematical Art, Menaechmus
related to External links · 13
Cubic equation → Cardano, Cardano's, EMS Press, Encyclopedia, Ferrari's, History, MacTutor, Mathematics, Mathologer, NOT, THE CUBIC FORMULA, What, YouTube
related to In mathematics · 13
Cubic equation → Angle, Bézier, Cauchy, Critical, Euler, Further, Given, In, Inflection, Intersection, Marden's, Steiner, The
related to Lagrange's method · 12
Cubic equation → Abel, Apart, Cardano's, In, Joseph Louis Lagrange, Lagrange, Lagrange's, Nevertheless, Ruffini, Réflexions, This, Thoughts
related to In other sciences · 8
Cubic equation → Charlot, In, Kepler's, Kinematic, Rayleigh, The, Van, Waals
related to Trigonometric solution for three real roots · 8
Cubic equation → François Viète, Galois, It, More, Nevertheless, Otherwise, This, When
related to Cardano's formula · 7
Cubic equation → Cardano's, Depressed, Ferro, Gerolamo Cardano, Niccolo Fontana Tartaglia, Scipione, The
related to Depressed cubic · 6
Cubic equation → Cubics, In, Let, The, They, Tschirnhaus
related to Factorization · 6
Cubic equation → By Gauss's, Finding, If, In, Such, The

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Important terminology

cubic roots displaystyle equation root real frac one equations formula coefficients complex depressed cube discriminant three 27 polynomial method two

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Newton's method.The coefficients do not need to be real numbersinstance ofusing Omar Khayyam's method.trigonometricallynumerical approximations of the roots can be found using root-finding algorithms0.80text
Reviel Netz dispute whether the Greeks were thinking about cubic equations or just problems that can lead to cubic equationsinstance ofthough historians0.80text
Cubic equationhas applicationCubic0.60section
Cubic equationrelated to Cardano's formulaGerolamo Cardano0.60section
Cubic equationrelated to Cardano's formulaScipione0.60section
Cubic equationrelated to Cardano's formulaFerro0.60section
Cubic equationrelated to Cardano's formulaNiccolo Fontana Tartaglia0.60section
Cubic equationrelated to Cardano's formulaThe0.60section
Cubic equationrelated to Cardano's formulaDepressed0.60section
Cubic equationrelated to Cardano's formulaCardano's0.60section
Cubic equationrelated to Depressed cubicCubics0.60section
Cubic equationrelated to Depressed cubicThey0.60section

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