Question 99
The real polynomial $\varphi(x) = ax^3 + bx^2 + cx + d$ has three positive roots, and $\varphi(0) \lt 0$. Prove that
$$
2b^3 + 9a^2d - 7abc \le 0. \quad \textcircled{1}
$$
$$
2b^3 + 9a^2d - 7abc \le 0. \quad \textcircled{1}
$$
MathNet 2008-part-01 — 165 problems (EN–VI) Question 99
Math Olympiad Vault · MathNet 2008-part-01 — 165 problems (EN–VI)