Cubic equation

A polynomial equation in one variable with degree three, commonly written as ax³ + bx² + cx + d = 0, where a is nonzero. Over the complex numbers, it has three roots counted with multiplicity.

Depressed cubic: A cubic equation with no squared term, written x³ + px + q = 0. A change of variable removes the quadratic term and simplifies solving.
Polynomial: An expression built from constants and variables using addition, subtraction, and nonnegative integer powers. A cubic equation is a polynomial equation of degree three.
Greek geometry: The mathematical tradition of ancient Greece, known for systematic geometric proofs and constructions. Early cubic problems arose from geometric constructions such as doubling the cube.
Cubic spline: A piecewise polynomial function whose segments are cubic and join smoothly at specified points. Cubic equations determine spline segments and their interpolation constraints.
Linear equation: An equation in which the variable has highest exponent one. A linear equation has one root at most, unlike a cubic's three roots counted with multiplicity.
Cardano's formula: A radical formula for solving general cubic equations. It expresses roots after reducing a cubic to depressed form.
Degree of a polynomial: The greatest exponent of the variable with a nonzero coefficient in a polynomial. The degree identifies a cubic by its highest nonzero power, three.
Doubling the cube: The classical construction problem of finding a cube whose volume is twice a given cube's. Its geometric reduction leads to a particular cubic equation that compass and straightedge cannot solve.
Cubic Bézier curve: A parametric curve defined by four control points and cubic Bernstein polynomials. Its coordinate equations are cubic polynomials in the curve parameter.
Quadratic equation: A polynomial equation in one variable with degree two. Quadratics have a simpler radical formula and at most two roots.

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