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2013 HMMT Algebra #5: Maximum Possible Coefficient

Source:

February 16, 2013
HMMTquadratics

Problem Statement

Let aa and bb be real numbers, and let rr, ss, and tt be the roots of f(x)=x3+ax2+bx−1f(x)=x^3+ax^2+bx-1. Also, g(x)=x3+mx2+nx+pg(x)=x^3+mx^2+nx+p has roots r2r^2, s2s^2, and t2t^2. If g(−1)=−5g(-1)=-5, find the maximum possible value of bb.
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