Exact solution to 6th degree poly

[matt271]

Greetings all,

If somebody can provide me the exact, real solution to the 6th degree poly between [sqrt(2)-1, 1/2], they will get a citation in my thesis.

64t^6 + 576t^5 + 2592t^4 + 3888t^3 - 26244t + 10935 = 0

Bonus points to anybody who recognizes the number.

That is all,
Thank You

[Brightguy]

The Galois group of that polynomial over Q is S6, which means that the polynomial not solvable by radicals, as well as irreducible, so no root is expressible by radicals.

In short, there is no exact expression using basic mathematical operations (+, −, ×, ÷, roots).

[bl0ckeduser]

Brightguy @ Sat Mar 10, 2012 2:18 pm wrote:

The Galois group of that polynomial over Q is S6, which means that the polynomial not solvable by radicals, as well as irreducible, so no root is expressible by radicals.

In short, there is no exact expression using basic mathematical operations (+, −, ?, ?, roots).

Hmm, and the rational roots theorem was no help

[matt271]

Ok thank you guys