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单词 QuadraticResolvent
释义

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

z2+qz-(p3)3=0

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

z1=u3,z2=v3

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

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

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更新时间:2025/5/4 1:23:38