Root[Function[z, Subscript[a, 0] + Subscript[a, 1] z + Subscript[a, 2] z^2 + Subscript[a, 3] z^3], k] == -(Subscript[a, 2]/(3 Subscript[a, 3])) + (E^((2 I Pi (k - 1))/3) p)/(3 2^(1/3) Subscript[a, 3]) - (2^(1/3) r)/(E^((2 I Pi (k - 1))/3) (3 p Subscript[a, 3])) /; p == (q + Sqrt[q^2 + 4 r^3])^(1/3) && q == 9 Subscript[a, 1] Subscript[a, 2] Subscript[a, 3] - 2 Subscript[a, 2]^3 - 27 Subscript[a, 0] Subscript[a, 3]^2 && r == 3 Subscript[a, 1] Subscript[a, 3] - Subscript[a, 2]^2 && 1 <= k <= 3

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2001-10-29