can someone explain this to me (1 Viewer)

[nike33]

why is it impossible to 'solve' ALL quintic equations? for example with quadratics you have a+b and ab and by solving simul you can find the zeros(if any), for cubics you have a+b+c, ab+ac+cb, abc and again solving 3 simul eqn's with 3 variables can be done with qunitics cant you get 5 equations with 5 variables ie (a+b+c+d+e, ab +ac +...., etc) so why cant you solve 5 simul equations to get the zeroes or is this impossible or something??

 

[turtle_2468]

so how exactly do you solve simultaneously? the point is, if you have a+b and ab, it's all well and fine, but the only way you get a, b is by solving the quadratic. You're confusing ability to solve n LINEAR simul eqn's in n variables with the ability to do it generally.... which doesn't exist. To be convinced of this, try to solve a general cubic (there is a moderately nice formula, half a line, but still hard to derive)
It IS possible to "solve" a quintic in terms of hypergeometric fns, but this isn't really what ppl mean by solving it... Quartics are possible in terms of polynomials, roots etc, although the actual formula would take something like half a gig of storage space...
Source: poster on my wall. (*sigh*... sad isn't it... at least it was free)

 

[Affinity]

quartics aren't that scary, I think turtle meant half a page
Cool poster turtle, where did you get it ?

 

[Xayma]

Originally posted by Affinity
quartics aren't that scary, I think turtle meant half a page
Cool poster turtle, where did you get it ?

No I think he meant the general formula for quartics. Quintics there is no general solution for (it was proved sometime)

 

[Affinity]

Precisely, the general formula isn't that long

 

[jm1234567890]

Originally posted by Xayma
No I think he meant the general formula for quartics. Quintics there is no general solution for (it was proved sometime)

no, you wrong, its the 6-tics, whatever you call them that have no general somution

 

[Affinity]

^......Hmm.. no

 

[CM_Tutor]

The solution of the general quartic, if anyone is interested is:

Consider an equation of the form x⁴ + Bx³ + Cx² + Dx + E = 0

Find a = alpha, any REAL root of the cubic y³ - Cy² + (BD - 4E)y + 4(CE - D² - B²E) = 0

The solutions of the quartic are then the four roots of 2z² + (B +/- sqrt(B² - 4C + 4a)) + a +/- sqrt(a² - 4E) = 0

 

[Xayma]

And then you get to have fun and stick that in the quadratic formula

 

[jm1234567890]

http://library.wolfram.com/examples/quintic/main.html

grrr... i remembered wrong

 

[abdo]

No I think he meant the general formula for quartics. Quintics there is no general solution for (it was proved sometime)

wasn't it that scandinavian dude, abels who showed that? umm i really enjoyed reading about abels and galois, they are so much cooler than the evil gauss and cauchy

 

[turtle_2468]

Precisely, the general formula isn't that long

Scammed it from IMO2001 Also got another cool poster about reimann zeta fn... both on my bedroom wall... nerdy isn't it.. but one of them is getting tattered so coming off soon.
I did mean half a something.. let me go check
Oh. Yeah, quartic isn't excessively long, you're right affinity But in like 3 point font, so I can't tell how long it is.. I'll post it up if I'm bored tonight or if ppl want to see quartic one
It was Ruffini and Abel that proved impossibility..
The soln to the quintic in terms of elliptic functions takes around a terabyte of storage in terms of original coefficients

 

[turtle_2468]

wasn't it that scandinavian dude, abels who showed that? umm i really enjoyed reading about abels and galois, they are so much cooler than the evil gauss and cauchy

There's always newton and lagrange to go on..... and you thought soccer rivalry was bad..