MathDB
2b^3+ 9a^2 d - 7abc <= 0 for f(x) = ax^3 + bx^2 + cx + d, f(0) < 0

Source: 2009 Grand Duchy of Lithuania, Mathematical Contest p2 (Baltic Way TST)

October 3, 2020
algebraCubicinequalities

Problem Statement

Let f(x)=ax3+bx2+cx+df(x) = ax^3 + bx^2 + cx + d be a polynomial with real coefficients. Given that f(x)f(x) has three real positive roots and that f(0)<0f(0) < 0, prove that 2b3+9a2d−7abc≤02b^3+ 9a^2 d - 7abc \le 0.
Back to ProblemsView on AoPS