# Homework Help: Determine if sqrt(-3) is an element in a splitting field

1. May 15, 2010

### gop

1. The problem statement, all variables and given/known data

L is the splitting field generated by $$x^2+x+1$$ (over $$\mathbb{Q}$$)
a) Is $$\sqrt{-3}$$ an element of L?
b) Is $$sqrt(-3)$$ an element of $$\mathbb{Q}(a)$$, where $$a$$ is a complex root of $$x^3+x+1$$?

2. Relevant equations

3. The attempt at a solution

Really no idea.

2. May 15, 2010

### VeeEight

You should start by finding the roots of the given polynomials.