Formula for roots of higher polynomials?

Does anyone know of the formulas for roots of higher order polynomials (3+)?  We learned the quadratic formula in grade school but never heard of formulas for higher polynomials..  do they exist?

Do you know how the quadratic equation was calculated? If so complete the square except with..

ax^4 + bx^3 + cx^2 + dx + e = 0

They don't exist for most higher-order polynomials. They do for 3 and 4, though.

There's a very complicated one for cubics, and there's a super-duper complicated one for quartics. However, Niels Abel proved that no formula exists for quintics, and Evariste Galois proved that no formula exists for anything above quartics.

Just use Newton's method. It's easy, and it kicks ass.

>>4
What is the basic idea behind the proof that no formula exists for quintics and above?  In other words, what is the common characteristic of these equations that makes them formula-constructible for up to quartics inclusive, yet not beyond that complexity?

Making the 4th power of complexity the demarcation point just seems like an arbitrary thing.

>>5
http://en.wikipedia.org/wiki/Galois_theory#Application_to_classical_problems
'"Why is there no formula for the roots of a fifth (or higher) degree polynomial equation in terms of the coefficients of the polynomial, using only the usual algebraic operations (addition, subtraction, multiplication, division) and application of radicals (square roots, cube roots, etc)?"'

Read, and stop being such a quasi-philosophical tit.

>>5
The fact is the A_n is normal for n>5, and thus S_n contains a simple, normal subgroup.

The reason that makes the equations unsolvable, is touched on by the wiki page on "Galois theory", but I'm not entirely certain myself how it follows.

>>4

How do you use Newton's Method to find complex roots?

>>8
http://en.wikipedia.org/wiki/Newton_fractal

Kickin'.

>>7
Ahhh it's to do with that is it? One of my lecturers recently gave an awesome geometric proof of A_n's normality, based around the dodecahedron.

>>6
Before you know, you have to admit that you DON'T KNOW.  That's why I asked -- I just didn't know.  The hostility of your response is simply uncalled for and reveals a boorishness and lack of social skill.

Just the same, I'll read up on Galois Theory and attempt to sense why Quintics+ are not formulizable.  While I'm doing that, you should consider your error and how you should better interact with people in the future.  Good day.

>>11
Actually, I called you a tit because, seeing your pretentious posting history, you're basically a tit. Also:
"Making the 4th power of complexity the demarcation point just seems like an arbitrary thing."
Yes, I'm sure years of formal mathematical theory went into proving that something they made the hell up was true.

>>11

You have used the word "boorishness" in a sentence.  Your argument is invalid.

>>4
You make it sound like Abel's and Galois's results were different. They weren't; they were identical, but discovered independently (I think it was Galois's work that was ignored for quite a while). It's pretty easy to see that if there is no general solution to the quintic, there is no general solution to any degree greater than 4. Suppose there is a general solution for degree k > 4; then k >= 5. Given a 5th degree polynomial f(x), take x^(k-5)*f(x). This is kth degree, and therefore solvable with the general solution for degree k polynomials, but the solutions will be the solutions of f(x) along with k-5 0's.

>>12
Actually, you called me a tit since you despise open inquiry and fairly well give blowjobs to prominent math icons as a form of hero worship.  Real scholarship is egoless.  It's going to take a lot of time for you to understand that, I can tell.

As for what is formal and that is true, I merely noted that the demarcation point seems arbitrary.  I didn't say that it WAS ... only that it seemed.  That's a part of free inquiry -- which we've established you despise while your mouth is O-ring sealed around the cock of a Nobel Laureate.

In the future, just try to suspend that pointless ego of yours and just relate the information as you purport to understand it.  That's why these called these things "message boards".  You've been sending another message entirely.

While we're on the topic of what you purportedly understand, can you even RELATE in any terms whatsoever what the Galois Theory is?  Pointing to a wiki is a great way to show that you really don't understand the conclusive structure in the first place.  In fact, anyone who is unable to relate in lesser terms what they supposedly know about higher organization, probably doesn't even understand the topic in the first place.  People who truly understand something, largely are able to deliver instruction in that topic to a wider audience.  You've failed to do that.  My reasonable conclusion about that is obvious.

>>15
This is math, not science, so
Nobel Laureate -> Field Medalist

>>10


Geometrical proofs aren't proofs, it's just pictures and hand waving.

>>17
Hehe, it wasn't that sort of geometric proof, but it did use the geometric properties of the shape. SORRY FOR THE CONFUSION EVERYONE.

>>16
Oops.  Thx.