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

[gop]

Homework Statement

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 $$x^3+x+1$$?

Homework Equations

The Attempt at a Solution

Really no idea.

 

[VeeEight]

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