MathDB
real roots of two plynomials

Source: 41-st Vietnamese Mathematical Olympiad 2003

March 10, 2007
algebrapolynomialalgebra proposed

Problem Statement

Define p(x)=4x3−2x2−15x+9,q(x)=12x3+6x2−7x+1p(x) = 4x^{3}-2x^{2}-15x+9, q(x) = 12x^{3}+6x^{2}-7x+1. Show that each polynomial has just three distinct real roots. Let AA be the largest root of p(x)p(x) and BB the largest root of q(x)q(x). Show that A2+3B2=4A^{2}+3 B^{2}= 4.
Back to ProblemsView on AoPS