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2017 Algebra Tiebreaker #3

Source:

September 10, 2022
2017Algebra Tiebreaker

Problem Statement

For some integers bb and cc, neither of the equations below have real solutions: \begin{align*} 2x^2+bx+c&=0\\ 2x^2+cx+b&=0. \end{align*} What is the largest possible value of b+cb+c?