Algebra Level 5

$\large f(x)=ax^2 - (3 + 2a)x + 6, \quad a\ne 0$

If the set of values of $$a$$ for which $$f(x)$$ is postive for exactly three distinct negative integral values of $$x$$ is $$(c,d]$$, then find the value of $$c^2 + 16d^2$$.

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