The solution of the cubic equations.  The general cubic equation  [Graphics:Images/FunTheoremAlgebraMod_gr_39.gif] has roots

[Graphics:Images/FunTheoremAlgebraMod_gr_40.gif]

[Graphics:Images/FunTheoremAlgebraMod_gr_41.gif]

[Graphics:Images/FunTheoremAlgebraMod_gr_42.gif]

 

Exploration.

Enter the general cubic equation.

[Graphics:../Images/FunTheoremAlgebraMod_gr_43.gif]

[Graphics:../Images/FunTheoremAlgebraMod_gr_44.gif]


The formulas for the roots [Graphics:../Images/FunTheoremAlgebraMod_gr_45.gif] are complicated.  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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