Example of using Cardano's formula for cubic equations.

In the following text all values were computed using module "Cubic Functions" of program "Ruler and Compass". You can Download "Ruler and Compass" version 1.5 or learn more about module "Cubic Functions".

Let us consider a cubic function:



This function is reducible and has a root equal -1. Second root is


and third root is conjugate to a second one.

Using Cardano's formula computer received first root (which is equal -1) as



There is no error. The last fraction is equal -1, although it is very hard to see this.
The same situation occurs with respect to a second root. Computer shows second root to be equal


which is much more complex than it should be.
Here w denotes a root of 1 of degree 3

This shows that using Cardano's formulas not always leads to the best results.