3rd order equations



On 16/08/2013 10:56 PM, Esben Byskov wrote:
> *Maybe somebody can help.
>
> I have tried to solve the following rather simple equation using maxima:
>
> (%i1) Eq: -2*q^3+3*q-1.357008100494576;
> (%o1)                  - 2 q  + 3 q - 1.357008100494576
> *

> ***A plot of Eq shows that there is at least one real root at
> about -1.40.  Therefore the above result bothers me. * 

The advice about floating point vs symbolic solution certainly applies 
in this case.  In addition, it is worth remembering that it is not 
always possible to express the solutions of a cubic equation with 
integer (or rational) coefficients that have three real roots in terms 
of radicals using only real expessions.

For more information, search for "casus irreducibilis".