Ok I'm pretty sure that not even X^4+x^3+x^2+x+1 has any real solution. So I guess there are 4 more complex solutions. So I was thinking about (ax^2+bx+c)(dx^2+ex+f) and trying to come up with some values for a, b, c, d, e and f but it seems to don't work...
Any idea??
I have to find the complex zeros of the following polynomial:
x^6+x^4+x^3+x^2+1
This evidently doesn't have any real solution so I tried to facto it with long division and by guessing I came up with:
(x^2-x+1)(x^4+x^3+x^2+x+1)
How can I factor the 4th degree polynomial now? Or how can I...