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Root






Mathematica Notation

Traditional Notation









Elementary Functions > Root[polynomialInzk] > Specific values > Specialized values





http://functions.wolfram.com/01.33.03.0005.01









  


  










Input Form





Root[Function[z, Subscript[a, 0] + Subscript[a, 1] z + Subscript[a, 2] z^2 + Subscript[a, 3] z^3 + Subscript[a, 4] z^4], k] == -(Subscript[a, 3]/(4 Subscript[a, 4])) + (2 Floor[(k - 1)/2] - 1) Subscript[\[Epsilon], 1] + (-1)^k (1 - UnitStep[k - 3]) Subscript[\[Epsilon], 2] - (-1)^k (UnitStep[2 - k] - 1) Subscript[\[Epsilon], 3] /; Subscript[\[Epsilon], 1] == (1/2) Sqrt[(2^(1/3) (Subscript[a, 2]^2 - 3 Subscript[a, 1] Subscript[a, 3] + 12 Subscript[a, 0] Subscript[a, 4]))/ (3 s Subscript[a, 4]) + (3 Subscript[a, 3]^2 + 2 2^(2/3) s Subscript[a, 4] - 8 Subscript[a, 2] Subscript[a, 4])/ (12 Subscript[a, 4]^2)] && Subscript[\[Epsilon], 2] == (1/2) Sqrt[u + v] && Subscript[\[Epsilon], 3] == (1/2) Sqrt[u - v] && u == -((2^(1/3) s^2 + 2 Subscript[a, 2]^2 - 6 Subscript[a, 1] Subscript[a, 3] + 24 Subscript[a, 0] Subscript[a, 4])/ (2^(2/3) s Subscript[a, 4])) + 8 Subscript[\[Epsilon], 1]^2 && v == (Subscript[a, 3]^3 - 4 Subscript[a, 2] Subscript[a, 3] Subscript[a, 4] + 8 Subscript[a, 1] Subscript[a, 4]^2)/ (8 Subscript[a, 4]^3 Subscript[\[Epsilon], 1]) && s == (t + 2 Subscript[a, 2]^3 - 9 Subscript[a, 2] (Subscript[a, 1] Subscript[a, 3] + 8 Subscript[a, 0] Subscript[a, 4]) + 27 (Subscript[a, 0] Subscript[a, 3]^2 + Subscript[a, 1]^2 Subscript[a, 4]))^(1/3) && t == Sqrt[-4 (Subscript[a, 2]^2 - 3 Subscript[a, 1] Subscript[a, 3] + 12 Subscript[a, 0] Subscript[a, 4])^3 + (2 Subscript[a, 2]^3 - 9 Subscript[a, 2] (Subscript[a, 1] Subscript[a, 3] + 8 Subscript[a, 0] Subscript[a, 4]) + 27 (Subscript[a, 0] Subscript[a, 3]^2 + Subscript[a, 1]^2 Subscript[a, 4]))^2] && 1 <= k <= 4










Standard Form





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MathML Form







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Rule Form





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Date Added to functions.wolfram.com (modification date)





2001-10-29





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