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

Let F be a field and let E be an extension field of F. Let [itex]\alpha[/itex] be an element of E that is algebraic over E. Is it true thatallof the zeros of [itex]irr(\alpha,F)[/itex] are contained in the extension field [itex]F(\alpha)[/itex]?

EDIT: I mean algebraic over F

2. Relevant equations

3. The attempt at a solution

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# Extension fields

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