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Let $F$ a field and let $D$ an element of an extension $K/F$ such that $D$ is not the square of any element of $F$. Does there exists an irreducible polynomial in $F[X]$ with discriminant $D$? Are there sufficient conditions for such polynomial to exists e.g. $char F\neq 2$?

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Do you mean $\sqrt{D}\in K$? –  Alex Becker May 8 at 22:39
    
@AlexBecker Not necessarily but if the statement is true under some conditions it might be one them. It is not an exercise. –  Test123 May 9 at 4:19

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