Problem #PRU-61038

Problems Algebra Polynomials Cubic polynomials Symmetrical polynomials Vieta's Formulas

Problem

Let it be known that all the roots of some equation \(x^3 + px^2 + qx + r = 0\) are positive. What additional condition must be satisfied by its coefficients \(p, q\) and \(r\) in order for it to be possible to form a triangle from segments whose lengths are equal to these roots?