Thread: Roots of a 3rd degree polynomial

Hi,

I think I heard of formulae that directly get you the roots of a degree 3 polynomial. I mean, like the ones of a degree 2 which are

(-b + or - (b^2 - 4 ac)^1/2) / 2a

I'm posting this question because I need them like that, in symbols. I don't care about the numerical value since I can get it using my calculator.

Thanks very much.

The formula is not pretty - dpmms does the whole derivation thing which is always a good place to start

http://www.dpmms.cam.ac.uk/~wtg10/cubic.html

The formula is not pretty at all! I cannot work with that one.

I guess I will try to find a different approach...

Thanks for the link.

pretty? all formulas are pretty. They are just less or more simple

Simplicity is beautiful, complexity interesting. Personal opinion.

Logic is beautiful
Therefor correct math is beutifull
Therefor is physics beutifull

Originally Posted by Stranger

The formula is not pretty at all! I cannot work with that one.

I guess I will try to find a different approach...

Thanks for the link.

Well you formula's for everything up to the quartic and if you limit yourself to only taking roots then thats were you stop (Galois Theory 101) though an asymptotic expansion for a cubic with small leading co-efficient is usually suffient for most physcial applications. Why do you want a formula?

Originally Posted by Zelos

pretty? all formulas are pretty. They are just less or more simple

Lol - ive seen some really ugly formula before, just start expaning Einsteins field equations in simple cartesian co-ordinates with out any symmetry considerations!

Zelos is just being a smartass. :P

all hail zelos

If you guys think the solution to the cubic is not pretty, has anyone seen the solution to the quartic? Degree 4? That's insane. So insane I forgot it.

Originally Posted by Absane

If you guys think the solution to the cubic is not pretty, has anyone seen the solution to the quartic? Degree 4? That's insane. So insane I forgot it.

The Quartic Formula

From that same page, lol:

The formulas for the roots are much too unwieldy to be used for solving quartic equations by radicals, even with the help of a computer.

Originally Posted by Elbethil

Originally Posted by Absane

If you guys think the solution to the cubic is not pretty, has anyone seen the solution to the quartic? Degree 4? That's insane. So insane I forgot it.

The Quartic Formula

From that same page, lol:

The formulas for the roots are much too unwieldy to be used for solving quartic equations by radicals, even with the help of a computer.

I don't know.. that seems like a lot more than I had to do. I just remember having to solve these by hand last year

And I thought the cubic was enough work...