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

  1. May 15, 2010 #1

    gop

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

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


    2. Relevant equations


    3. The attempt at a solution

    Really no idea.
     
  2. jcsd
  3. May 15, 2010 #2
    You should start by finding the roots of the given polynomials.
     
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