Suppose \(\alpha, \beta,\) and \(\gamma\) are the roots of polynomial \(x^{3} + px^{2} + qx + 2 = 0 \) and that \(\alpha \beta + 1 = 0\). What is the value of \(2p + q + 100\)?

This problem is shared by Prakkash M, who came across it in his Mathematical Olympiad Training.

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