(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))

Printable View

- Jul 27th 2010, 12:21 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)) - Jul 27th 2010, 12:40 PMeumyang
Hmm, are you the OP in this thread from the Math Is Fun forum?

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

(Wondering) - Jul 27th 2010, 12:52 PMchiph588@
Rational Root Theorem. This tells you there are no linear factors.

- Jul 27th 2010, 12:54 PMAlso sprach Zarathustra
Maybe by using calculus...

- Jul 27th 2010, 03:54 PMmelese
- Jul 27th 2010, 03:59 PMchiph588@
- Jul 27th 2010, 04:55 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 .