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

			(3)
			(4)
			(5)

The roots , , and  of  are given in terms of the roots , , , and  of  by

			(6)
			(7)
			(8)

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.