# (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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