Problem

Source: Vietnam TST 2024 P4

Tags: algebra, polynomial, inequalities



Let α(1,+) be a real number, and let P(x)R[x] be a monic polynomial with degree 24, such that (i) P(0)=1. (ii) P(x) has exactly 24 positive real roots that are all less than or equal to α. Show that |P(1)|(195)5(α1)24.