MathDB

Values of p(1)

Source: Baltic way 2009

November 11, 2009

algebrapolynomialfunctioninequalitiesalgebra proposed

Problem Statement

A polynomial

p(x)

of degree

n\ge 2

has exactly

n

real roots, counted with multiplicity. We know that the coefficient of

x^n

1

, all the roots are less than or equal to

1

, and

p(2)=3^n

. What values can

p(1)

take?