Question 158
Let $\alpha \in (1, +\infty)$ be a real number, and let $P(x) \in \mathbb{R}[x]$ 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 $\alpha$.
Show that $|P(1)| \le \left(\frac{19}{5}\right)^5 (\alpha - 1)^{24}$.
(i) $P(0) = 1$.
(ii) $P(x)$ has exactly $24$ positive real roots that are all less than or equal to $\alpha$.
Show that $|P(1)| \le \left(\frac{19}{5}\right)^5 (\alpha - 1)^{24}$.