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Find the fourth root of the equation

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October 7, 2010
trigonometryfunctionalgebra proposedalgebra

Problem Statement

Three of the roots of the equation x4−px3+qx2−rx+s=0x^4 -px^3 +qx^2 -rx+s = 0 are tan⁡A,tan⁡B\tan A, \tan B, and tan⁡C\tan C, where A,BA, B, and CC are angles of a triangle. Determine the fourth root as a function only of p,q,rp, q, r, and s.s.
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