- Thread starter
- Moderator
- #1

- Jan 26, 2012

- 995

-----

**Problem**: Let $\theta$ be a root of $x^3-3x+1$. Prove that the splitting field of this polynomial is $\mathbb{Q}(\theta)$ and that the Galois group is cyclic of order $3$. In particular the other roots of this polynomial can be written in the form $a+b\theta+c\theta^2$ for some $a,b,c\in\mathbb{Q}$. Determine the other roots explicitly in terms of $\theta$.

-----

Remember to read the POTW submission guidelines to find out how to submit your answers!