MathDB

polynom with coefficient 0 or 1

Source: Azerbaijan NMO 2024. Senior P4

July 8, 2024

algebrapolynomialAZE SENIOR NATIONAL MO

Problem Statement

Let

P(x)

be a polynomial with the coefficients being

0

1

and degree

2023

. If

P(0)=1

, then prove that every real root of this polynomial is less than

\frac{1-\sqrt{5}}{2}