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Re: Explicit solution to Root[]


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
about the quintic equation here:
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[66]:=
N[Root[-24 + 6*#1 + 51*#1^2 - 40*#1^3 - 54*#1^4 + 54*#1^5 &, 1, 0]]

Out[66]=
1.11221

In[70]:=
ToSymbolic[Root[-24 + 6*#1 + 51*#1^2 - 40*#1^3 - 54*#1^4 + 54*#1^5 &,
1]];

In[71]:=
N[%]

Out[71]=
{1.11221}


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