Question 42
Let $f(x) = x^n + a_1x^{n-1} + \cdots + a_n$ be a polynomial of degree $n \ge 2$ with real roots $b_1, b_2, \ldots, b_n$. If $x$ is greater than $b_1, b_2, \ldots, b_n$, prove that
$$
f(x+1) \left( \frac{1}{x-b_1} + \frac{1}{x-b_2} + \cdots + \frac{1}{x-b_n} \right) \ge 2n^2.
$$
$$
f(x+1) \left( \frac{1}{x-b_1} + \frac{1}{x-b_2} + \cdots + \frac{1}{x-b_n} \right) \ge 2n^2.
$$