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2013 preRMO p16, common root, x^3 - 3x + b=0, x^2 + bx -3=0

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August 8, 2019
SumalgebraRoot

Problem Statement

Let f(x)=x3−3x+bf(x) = x^3 - 3x + b and g(x)=x2+bx−3g(x) = x^2 + bx -3, where bb is a real number. What is the sum of all possible values of bb for which the equations f(x)f(x) = 0 and g(x)=0g(x) = 0 have a common root?
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