(Angry)How can I prove that you can not solve the polynomial : x^8-x^7+x^5-x^4+x^3-x+1

Over Q

(No use by Eisenstein theorem , without using polynomial Cyaklotomi))

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- July 27th 2010, 01:21 PMrtrt1polynomial
(Angry)How can I prove that you can not solve the polynomial : x^8-x^7+x^5-x^4+x^3-x+1

Over Q

(No use by Eisenstein theorem , without using polynomial Cyaklotomi)) - July 27th 2010, 01:40 PMeumyang
Hmm, are you the OP in this thread from the Math Is Fun forum?

http://www.mathisfunforum.com/viewtopic.php?pid=146808

(Wondering) - July 27th 2010, 01:52 PMchiph588@
Rational Root Theorem. This tells you there are no linear factors.

- July 27th 2010, 01:54 PMAlso sprach Zarathustra
Maybe by using calculus...

- July 27th 2010, 04:54 PMmelese
- July 27th 2010, 04:59 PMchiph588@
- July 27th 2010, 05:55 PMmelese
Here's what I meant.

According to the Rational Root Theorem:

Let be a polynomial equation with integer coefficients. If has a rational root , with relatively prime integers, then and . (Statement found in PlanetMath: rational root theorem)

In our case, and . Assume there is a rational root , then and . Now, , and so . (Two case after all!)

Checking the case we have and , contradicting .