quadratic resolvent

The quadratic resolvent of the cubic equationMathworldPlanetmath

y3+py+q=0, (1)

where p and q are known complex numbersMathworldPlanetmathPlanetmath, is the auxiliary equation


determining as its roots (http://planetmath.org/Equation)


the numbers u and v whose sum  y=u+v  satisfies the equation (1).  See example of solving a cubic equation (http://planetmath.org/exampleofsolvingacubicequation).

Analogically, a quartic equationMathworldPlanetmath has a cubic resolvent (resolvent cubicMathworldPlanetmath) equation.

Title quadratic resolvent
Canonical name QuadraticResolvent
Date of creation 2014-11-27 16:05:30
Last modified on 2014-11-27 16:05:30
Owner pahio (2872)
Last modified by pahio (2872)
Numerical id 9
Author pahio (2872)
Entry type Definition
Classification msc 12D10
Synonym quadratic resolvent equation
Related topic CardanosFormulae
Related topic TchirnhausTransformations
Defines cubic resolvent
Defines resolvent equation