SE-SKOLORNAS 1970 Problem 4

Let $p(x) = (x- x_1)(x- x_2)(x- x_3)$ , where $x_1, x_2$ and $x_3$ are real. Show that $p(x) p''(x) \le p'(x)^2$ for all $x$ .

Dataset text AI-MO AoPS. Quoted with source.

Solutions

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