Resolvent Cubic
For a given monic quartic equation
 |
(1) |
the resolvent cubic is the monic cubic polynomial
 |
(2) |
where the coefficients 
are given in terms of the 
by
The roots 
, 
, and 
of 
are given in terms of the roots 
, 
, 
, and 
of 
by
The resolvent cubic of a quartic equation can be used to solve for the roots of the quartic in terms of the roots of the cubic, which can in turn be solved for using the cubic equation.
See also
Cubic Equation, Quartic Equation
This entry contributed by David Terr
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Cite this as:
Terr, David. "Resolvent Cubic." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/ResolventCubic.html