Problem

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Tags: real analysis



Let $f:[a,b] \rightarrow \mathbb{R}$ a function with Intermediate Value property such that $f(a) * f(b) < 0$. Show that there exist $\alpha$, $\beta$ such that $a < \alpha < \beta < b$ and $f(\alpha) + f(\beta) = f(\alpha) * f(\beta)$.