how do you solve something like this:

123x^4+123x^2-433=0

I forgot how to do algebra

11/5/2005 4:27:03 PM

for polynomials over degree three, there is no closed form "general solution" analogous to the quadratic equation. that said...

unity% maple
|\^/| Maple 7 (SUN SPARC SOLARIS)
._|\| |/|_. Copyright (c) 2001 by Waterloo Maple Inc.
\ MAPLE / All rights reserved. Maple is a registered trademark of
<____ ____> Waterloo Maple Inc.
| Type ? for help.

> solve(123*x^4+123*x^2-433=0,x):

> evalf(%);
-1.200721669, 1.200721669, -1.562604404 I, 1.562604404 I


ugly, but true.

edit: for the exact solution, just replace that : with a ; -- i couldn't format it well enough to post, so oh well.

[Edited on November 5, 2005 at 5:13 PM. Reason : asdf]

11/5/2005 5:11:05 PM

Actually, it's polynomials of degree 5 or more that don't have a general, basic algebra solution. Degree four or less can always be done (though it may be tedious).

Here are a couple of examples of solving quartic polynomials:

http://www.1728.com/quartic2.htm

However, this one's not so bad. Just substitute u=x^2 and you've got a quadratic. Solve for u, then substitute back and solve for x.

11/5/2005 5:25:23 PM

^ i was just about to post with a correction..i looked it up in mathworld and saw that. thanks(!)

i was also going to post http://www.1728.com/quartic2.htm.

whoops!

11/5/2005 5:26:48 PM

thanks

11/5/2005 5:55:33 PM