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Show that the splitting field of a quadratic polynomial P(x) = Ax^x + Bx + C, with zeros [tex]\alpha[/tex] and [tex]\alpha^{'}[/tex] is [tex]V_\alpha[/tex] = Q*1 + Q * [tex]\alpha[/tex]. Q is of course the set of rationals.

I know I must be missing something here cause I also have problems trying to figure this out:

Suppose P(x) is a quadratic polynomial with zeroes [tex]\alpha[/tex] and [tex]\alpha^{'}[/tex], Prove that Q*1 + Q*[tex]\alpha[/tex] = Q*1 + Q*[tex]\alpha^{'}[/tex]

To me the zeros of a polynomial are related numbers but are different and thus should yield different vector spaces. These problems say they are the same vector space. Can anyone expand upon this?

Tex doesn't seem to work in preview but I could not see what was wrong with my notation from your tutorials. If you don't see anything an ascii version will soon follow.

Thanks.