27

Part of 1988 IMO Longlists

Problems(1)

Condition for the roots to be exactly the cosines

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

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

r

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

trigonometryalgebrapolynomialVietafunctionalgebra unsolved