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Suppose we want to find a polynomial whose splitting field is $\Bbb Q(\sqrt{2}, \sqrt{-3})$ over $\Bbb Q$. Then the following is how you'd do it right ?

We want to adjoin the roots $\alpha=\sqrt{2}, \beta=\sqrt{-3}$. so we could just say $(x^2-2)(x^2+3)=0$ and expanding the brackets gives the polynomial .

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    $\begingroup$ Yes, that's exactly how I would do it. $\endgroup$ – Lord Shark the Unknown Mar 8 at 18:57

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