MathDB

4

Part of 2007 Bosnia Herzegovina Team Selection Test

Problems(1)

Polynomial inequality

Source: Bosnia and Herzegovina TST 2007 day 2 problem 1

5/13/2014
Let P(x)P(x) be a polynomial such that P(x)=x3−2x2+bx+cP(x)=x^3-2x^2+bx+c. Roots of P(x)P(x) belong to interval (0,1)(0,1). Prove that 8b+9c≤88b+9c \leq 8. When does equality hold?
algebrapolynomialinequalitiesVietaalgebra unsolved