Vietnam NMO 2002_4
Source:
October 26, 2008
algebrapolynomialinequalities unsolvedinequalities
Problem Statement
Let , , be real numbers for which the polynomial x^3 \plus{} ax^2 \plus{} bx \plus{} c has three real roots. Prove that 12ab \plus{} 27c \le 6a^3 \plus{} 10\left(a^2 \minus{} 2b\right)^{\frac {3}{2}} When does equality occur?