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 x3+px2+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?