The solution of the quartic equations.  Mathematica can construct the solutions to the general quartic equation.

 

Exploration.

Enter the general quartic equation.

[Graphics:../Images/FunTheoremAlgebraMod_gr_61.gif]








[Graphics:../Images/FunTheoremAlgebraMod_gr_62.gif]
[Graphics:../Images/FunTheoremAlgebraMod_gr_63.gif]
[Graphics:../Images/FunTheoremAlgebraMod_gr_64.gif]
[Graphics:../Images/FunTheoremAlgebraMod_gr_65.gif]
[Graphics:../Images/FunTheoremAlgebraMod_gr_66.gif]
[Graphics:../Images/FunTheoremAlgebraMod_gr_67.gif]
[Graphics:../Images/FunTheoremAlgebraMod_gr_68.gif]
[Graphics:../Images/FunTheoremAlgebraMod_gr_69.gif]
[Graphics:../Images/FunTheoremAlgebraMod_gr_70.gif]
[Graphics:../Images/FunTheoremAlgebraMod_gr_71.gif]


The formulas for the roots [Graphics:../Images/FunTheoremAlgebraMod_gr_72.gif] are extremely complicated.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) 2006 John H. Mathews, Russell W. Howell