minimum and local maximum
Source: Ukrainian TST 2007 problem 8
September 19, 2007
algebrapolynomialinequalitiesinequalities proposed
Problem Statement
is polynomial with real coefficients. F(x) \equal{} x^{4}\plus{}a_{1}x^{3}\plus{}a_{2}x^{2}\plus{}a_{1}x^{1}\plus{}a_{0}. is local maximum and is minimum. Prove that \frac{3}{10}(\frac{a_{1}^{2}}{4}\minus{}\frac{2a_{2}}{3^{2}})^{2}< M\minus{}m < 3(\frac{a_{1}^{2}}{4}\minus{}\frac{2a_{2}}{3^{2}})^{2}