Re: Quartic Equation: do you know a procedural way to solve it ?

You didn't answer Edgar's question, which is what
form your want the solutions expressed in (approximate
form or exact form). Either way, once you have the
four roots, it's going to be the case that the original
quartic factors as four "x - root" factors (this is the
high school / college algebra factor theorem). Also, there
are ways of solving quartics that result in the roots being
expressd in terms of trig. functions of the coefficients
and in terms of hyperbolic trig. functions of the coefficients
(both in exact form). If these would serve for your purpose,
you might look into doing this, as I think the process
is simpler. The drawback is that the roots are expressed in
"less explicit form" due to bringing trig. functions onto
the scene, which are considered "less elementary" than
algebraic expressions involving radicals and arithmetic
operations.

Thanks for the clarification.
I'm a little bit confused about the "exact vs approximation" methods
to solve quartic equations.
I've found something about this googling around, but I did not
understand exactly the difference between two methods.
Does it mean that with a method rather than the other, you find
different solutions? Sound strange to me.

What I'm looking for is a method to find a 3D distance from a torus
with a line, that's why I need to solve a quartic equation. I don't
really know what is the best method to find the exact solution.

In any event, the formulas and methods are quite a bit
more elaborate than is the case with quadratic equations.
In fact, some of the better known methods for solving
quartic equations involve having to solve an auxiliary
cubic equation, so you'd probably want to first work on
solving cubic equations.

I've already wrote the code for solving cubic equations, it's working
good (it's easier).

Thank you.

--
Iacopo
.