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)∣≤(519)5(α−1)24. algebrapolynomialinequalities