Complex numbers, rational functions, logarithms, sequences and series, matrix operations, etc.

I have x^6 - 1=0
After the rational roots test, I have the factors of (x+1)(x-1).
So, after doing the synthetic division with these factors I am left with x^4 + x^2 + 1.
Now I am stuck. This equation does not factor, and it is not a quadratic. How do I move forward from here?
The roots by the way are 1,-1, and one plus or minus square root of 3 i divided by two and negative one plus or minus square root of 3 i divided by two. Please help!
rogermiranda

Posts: 19
Joined: Fri Apr 30, 2010 6:01 pm

Have you covered deMoivre's formula yet? Or are you maybe supposed to solve the "quadratic" (x2)2 + (x2) + 1, and then solve the quadratics that result?

stapel_eliz

Posts: 1784
Joined: Mon Dec 08, 2008 4:22 pm

rogermiranda wrote:I have x^6 - 1=0
After the rational roots test, I have the factors of (x+1)(x-1).
So, after doing the synthetic division with these factors I am left with x^4 + x^2 + 1.
Now I am stuck. This equation does not factor, and it is not a quadratic. How do I move forward from here?
...

$x^4 + x^2 + 1=(x^2+x+1)(x^2-x+1)$

Martingale

Posts: 363
Joined: Mon Mar 30, 2009 1:30 pm
Location: USA