(ITA) Double Polynomial

Level pending

Consider the polynomial \(P(m) + 3m + 18 = \alpha m \), where \(\alpha\) is a real constant such that the sum of all roots of \(P\) equals \(3\).

Evaluate the root \(m\) such that two, and only two, roots of the polynomial \(Q(n) = n^3 +m^{}n^2 + (m+4)n + 5 = 0\) are in the open interval \((-2, 2)\).

This problem was adapted from ITA's 2013 Math Paper.

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