History Of Polynomial Equations
Cubic - Page One


 

This equation is easily turned into a quadratic equation in by multiplying through by to obtain
(w^3)^2 - q(w^3) - 1/27 p^3 = 0

The result from the quadratic equation is
long and mighty solution

There are therefore six solutions for w (two corresponding to each sign for each root of w3). Plugging w back in to the reduced cubic above gives three pairs of solutions, but each pair is equal, so there are three solutions to the cubic equation.

1 - History
2 - Quadratics
3 - Cubic
4 - Quartic
5 - Quintic
6 - Appendix


Part Three: Solving The Cubic
Step One: Parameters Of The Cubic:
 x3 +  x2 +  x +  = 0


Step Two:


Step Three: Solutions:
x1 = 

x2 = 

x3 = 

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by thomas m. bösel @ www.vimagic.de for University Of Adelaide - History Of Mathematics 2002