Let \(f(x)\) be a non-constant real valued polynomial function such that at the point \(a\) we have \(f(a)^2+f'(a)^2=0\). Find the value of

\[\lim_{x \to a} \dfrac{f(x)}{f'(x)} \cdot \left\lfloor \dfrac{f'(x)}{f(x)} \right\rfloor\]

Note: \(f'(x) = \dfrac{d}{dx} f(x)\)

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