cubic equation

mathematics

Written by

The Information Architects of Encyclopaedia Britannica

Last updated

June 25, 2026

Quick Summary

A cubic equation is a polynomial equation where the highest sum of the exponents of variables in any term is three. This means the equation involves terms with variables raised to the power of three, such as (x^3).1

The study of solving equations, including cubic equations, has a long history in mathematics. By the late 16th century, mathematicians like Girolamo Cardano made significant contributions to understanding how to solve cubic and quartic equations. However, finding general solutions for equations beyond the fourth degree using radical methods proved impossible, as demonstrated by mathematicians like Paolo Ruffini and Niels Henrik Abel. The concept of a "root" in mathematics refers to a solution to an equation.234

Summary created from Britannica articles using AI. AI can make mistakes, so verify using Britannica articles.

4 Britannica Sources

Ask Britannica AI about this topic

Britannica doesn't have a full article on this topic, so we've curated a list of our relevant coverage.

- discriminant
  …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…
  Read More
  …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…
  Read More