 Irreducible polynomial in characteristic zero is separable (source code)

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= Irreducible polynomial in characteristic zero is separable

If $f$ is irreducible over a field of characteristic zero, then $f'\ne0$ and $\deg f'<\deg f$. Thus $f$ cannot divide $f'$, so irreducibility gives $\gcd(f,f')=1$. Consequently $f$ has no repeated root in any extension field.

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