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Algebra Level 5

Let \(\alpha,\beta\) and \(\gamma\) be the positive roots of the cubic equation \(x^3-ax^2+bx-c = 0 \) such that \(\alpha + 2\beta + 3\gamma =4 \) and \(81\alpha \beta\gamma = 32\).

Given that the value of \(b\) can be expressed as \( \dfrac pq\), where \(p\) and \(q\) are coprime positive integers, find \(5q - 2p \).

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