# 185 Followers Special!

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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