I know that the mathematics related to finding the general formula by expressing the roots of a third (and fourth) degree polynomial by means of radicals has had an impressive impact on mathematics (complex numbers and group theory, just to say).
However: are there any useful application of these formulas? My impression is that calculus (i.e. computing derivatives, bisection methods, Sturm theorem) are more useful both for qualitative and numerical properties of such roots even if a formula is available.
