MathDB
Finding Bounds on Roots

Source: ISI 2021 P7

July 18, 2021
algebracalculusinequalitiesBritishMathematicalOlympiad

Problem Statement

Let a,b,ca, b, c be three real numbers which are roots of a cubic polynomial, and satisfy a+b+c=6a+b+c=6 and ab+bc+ca=9ab+bc+ca=9. Suppose a<b<ca<b<c. Show that 0<a<1<b<3<c<4.0<a<1<b<3<c<4.
Back to ProblemsView on AoPS