The solution of the cubic equations.  Mathematica can construct the solutions to the general cubic equation. However they are quite formidable.

Exploration.

Enter the depressed cubic equation.

[Graphics:../Images/ComplexNumberOrigin_gr_120.gif]

[Graphics:../Images/ComplexNumberOrigin_gr_121.gif]

 

 

Enter the general cubic equation.

[Graphics:../Images/ComplexNumberOrigin_gr_122.gif]

[Graphics:../Images/ComplexNumberOrigin_gr_123.gif]

[Graphics:../Images/ComplexNumberOrigin_gr_124.gif]


The formulas for the roots [Graphics:../Images/ComplexNumberOrigin_gr_125.gif] are complicated.  Hopefully this text will promote their understanding.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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