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A determinant involving a polynomial is $0$
Let $n \geq 2$ and $f:\mathbb{R} \to \mathbb{R}, \: f(x)=(x-x_1)(x-x_2)\dots(x-x_n)$ where $x_1,\dots, x_n$ are distinct real numbers. The matrix $A=(a_{ij})_{1 \leq i,j \leq n}$ is defined as follows:...
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