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The cyclic quartic field generated by the fifth powers of the Lagrange resolvents of a dihedral quintic polynomial f(x) is explicitly determined in terms of a generator for the quadratic subfield of the splitting field of f(x). 2000 Mathematics Subject Classification: 11R16, 11R21. Let f(x) = x 5 +px 3 +qx 2 +rx+s ∈ Q[x] be an irreducible quintic polynomial with a solvable Galois group. Let x1,x2,x3,x4,x5 ∈ C be the roots of f(x). The splitting field of f is K = Q(x1,x2,x3,x4,x5). Letζ be a primitive fifth root of unity. The Lagrange resolvents of the root x1 are r1 = ( x1,ζ) = x1 +x2ζ +x3ζ 2 +x4ζ 3 +x5ζ 4 ∈ K(ζ), r2 = ( x1,ζ 2) = x1 +x2ζ 2 +x3ζ 4 +x4ζ +x5ζ 3 ∈ K(ζ), r3 = ( x1,ζ 3) = x1 +x2ζ 3 +x3ζ +x4ζ 4 +x5ζ 2 ∈ K(ζ), (1) r4 = ( x1,ζ 4) = x1 +x2ζ 4 +x3ζ 3 +x4ζ 2 +x5ζ ∈ K(ζ)