MathDB

Condition for the roots to be exactly the cosines

Source: IMO LongList 1988, Hong Kong 3, Problem 27 of ILL

October 22, 2005

trigonometryalgebrapolynomialVietafunctionalgebra unsolved

Problem Statement

Assuming that the roots of

x^3 + p \cdot x^2 + q \cdot x + r = 0

are real and positive, find a relation between

p,q

and

r

which gives a necessary condition for the roots to be exactly the cosines of the three angles of a triangle.