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Let p be an odd prime. Let f(x) ∈ Q(x) be an irreducible polynomial of degree...

Let p be an odd prime. Let f(x) ∈ Q(x) be an irreducible polynomial of degree p whose Galois group is the dihedral group D_2p of a regular p-gon. Prove that f (x) has either all real roots or precisely one real root.

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