Galois Group of Polynomial

Separable Polynomial
A polynomial over F is said to be separable if it has no multiple roots (i.e., all its roots are distinct).

Galois Group of Polynomial
Let f(x) be a separable polynomial over F. Let K be the splitting field over F of f(x). Then the Galois group of f(x) over F is defined to be \text{Gal}(K/F).

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