IMO 1983 LL USA68
Three of the roots of the equation x4 −px3 + qx2 −rx + s = 0
IMO 1983 LL USA68
Origin: USA
Problem
Three of the roots of the equation x4 −px3 + qx2 −rx + s = 0 are tan A, tan B, and tan C, where A, B, and C are angles of a triangle. Determine the fourth root as a function only of p, q, r, and s.