Problem

Source: Indonesia IMO 2010 TST, Stage 1, Test 5, Problem 2

Tags: algebra, polynomial, inequalities, algebra proposed



Consider a polynomial with coefficients of real numbers $ \phi(x)=ax^3+bx^2+cx+d$ with three positive real roots. Assume that $ \phi(0)<0$, prove that \[ 2b^3+9a^2d-7abc \le 0.\] Hery Susanto, Malang