Question

How does one solve the quartic? Hints please. (I know how to solve the cubic)

Answer 1

I know how to apply the Tschirnhaus transformation, also.

Answer 2

Here's a link to Euler's solution of the general quartic.

http://www.nickalls.org/wingspan/papers/maths/quartic2009.pdf

Answer 3

btw, @Directrix , who even learns this kind of thing in class?

Answer 4

the link won't work 0.o

Answer 5

@inkyvoyd --> Nobody I know except you. There's talk of the fascinating history with Tartaglia and Cardano.

Answer 6

But, I'm not learning it in class :S

Answer 7

Wow, that .pdf I just read has gone pfft.

Try this:

Proof of the Solution to the General Quartic Equation

Dec 9, 2006 – Proof of the Solution to the General Quartic Equation. In today's blog, I provide the proof for the solution of the general quartic equation.

http://fermatslasttheorem.blogspot.com/2006/12/proof-of-solution-to-general-quartic.html

Answer 8

You mean, when you gave me the link it worked, and when I tried it it died?

Answer 9

wth, that was the shortest complete proof of the quartic. Ever.

Answer 10

But, I found it. In so doing, I found who studies these things.

http://www.nickalls.org/contact.html
Click on RWD Nickalls

Selected publications

Scroll 2/3 the way down the page
Look for:
Mathematics (external links)
A new bound for polynomials when all the roots are real (2011).
The Mathematical Gazette (2011); vol 95 (November), 520-526 [PDF, 315 KB]
The quartic equation: alignment with an equivalent tetrahedron (2012).
The Mathematical Gazette (2012); vol 96 (March), 49-55 [PDF, 478 KB]
The quartic equation: invariants and Euler's solution revealed (2009).
The Mathematical Gazette (2009); vol 93, 66-75 [PDF, 550 KB] -----> This is it.
with Thomas Müller (2009)
Parameters for plotting a quartic.
A Wolfram demo using Mathematica (Wolfram Demonstration Project)
Visualising the quartic and its various resolvents.
--- A demo of the dynamic relationship between the quartic, its resolvent cubic (Euler's) and the resolvent quadratic.
[PDF, 1 MB]

Answer 11

Hey, I clicked on external links and got the "singing banana" who is talking about solving codes.
http://www.youtube.com/watch?v=iQhkoV_-8WI&feature=plcp

Answer 12

What?