Determine if sqrt(-3) is an element in a splitting field

[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.

[VeeEight]

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