Question 438947
In all aspects, ninth degree polynomials are quite ugly. The fact is, when you or I see the problem, we have absolutely no idea what any potential zeros could be. You could try the rational root test to knock off a few zeros, but it would take a very long time. In fact, the Abel-Ruffini theorem states that there is no general formula for a polynomial of degree 5 or higher.


Here is what WolframAlpha has to say:

http://www.wolframalpha.com/input/?i=2x^9+-+x^8+-+16x^7+%2B+17x^6+-+6x^5+-+5x^4+%2B+68x^3+-+77x^2+%2B+18+