Splitting field

Given a polynomial $p(x)\in Q[x]$, its splitting field is a field $K$ if $K$ is the smaller field that contains all the roots of $p(x)$.

Example

If $p(x)=x^4-5x^2+6$ then $K=Q(\sqrt{2},\sqrt{3})$

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Author of the notes: Antonio J. Pan-Collantes

antonio.pan@uca.es