       Re: Explicit solution to Root[]

• To: mathgroup at smc.vnet.net
• Subject: [mg58442] Re: Explicit solution to Root[]
• From: "Chris" <topher at csh.rit.edu>
• Date: Sat, 2 Jul 2005 04:07:02 -0400 (EDT)
• References: <da2mmv\$932\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Well, just typing it into Mathematica, I get it to reduce to:

Root[-24 + 6*#1 + 51*#1^2 - 40*#1^3 - 54*#1^4 + 54*#1^5 & , 1, 0]

Since it's the solution to a polynomial of degree 5, it's unlikely that
you'll get a nice clean solution with just radicals. You can find more
http://library.wolfram.com/examples/quintic/

If you want a symbolic answer, you can use a function I wrote called
ToSymbolic based off of the above link, but the answer is pretty
unwieldy.

http://www.csh.rit.edu/~topher/math/tosymbolic.html

In:=
N[Root[-24 + 6*#1 + 51*#1^2 - 40*#1^3 - 54*#1^4 + 54*#1^5 &, 1, 0]]

Out=
1.11221

In:=
ToSymbolic[Root[-24 + 6*#1 + 51*#1^2 - 40*#1^3 - 54*#1^4 + 54*#1^5 &,
1]];

In:=
N[%]

Out=
{1.11221}

```

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