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carcano
2024 Oct 10
0
Discriminant of a cubic polynomial
...tely, I do not know if any packages implement this functionality. Though, it is a topic that interests me.
Unlike the "classic discriminant", I prefer to work with the reduced polynomial. This "discriminant" is generalizable to a superset of Chebysev polynomials (which I called Cardano-polynomials).
x^3 - 3*c*x - 2*d = 0
x^5 - 5*c*x^3 + 5*c^2*x - 2*d = 0
x^7 - 7*c*x^5 + 14*c^2*x^3 - 7*c^3*x - 2*d = 0
discr = d^2 - c^n, where n = 3 for the degree 3 polynomial;
The beauty of this approach is that you can solve for all roots of these types of polynomials and the formula is much si...