Let f(x) be differentiable function and ...

Let f(x) be differentiable function and g(x) be twice differentiable function. Zeros of f(x), g'(x) be a, b, respectively, `(a lt b)`. Show that there exists at least one root of equation `f'(x) g'(x) + f(x) g''(x) = "0 on" (a, b)`.

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