3

Part of 1995 Hungary-Israel Binational

Problems(1)

Hungary-Israel Binational 1995_3

Source:

The polynomial f(x)\equal{}ax^2\plus{}bx\plus{}c has real coefficients and satisfies

\left|f(x)\right|\le 1

x\in [0, 1]

. Find the maximal value of |a|\plus{}|b|\plus{}|c|.

algebrapolynomialinequalities proposedinequalities