# Parabola

Calculus Level 4

Let $$f: [2, \infty) \mapsto [8, \infty)$$ be a surjective function given by

$\large f(x) = x^2 - (p-2) x + (3p - 2)$

where $$p \in \mathbb{R}$$. If the sum of all possible values of $$p$$ can be represented as $$a + b \sqrt{c}$$ where $$a, b$$ and $$c$$ are positive integers and $$c$$ is square free, then evaluate $$\dfrac{a}{bc}$$.

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