Game of Equations!

Algebra Level 5

\[\large{\begin{cases} x^3 + ax^2 + bx + c = 0 \\ x^3 + bx^2 + cx + a = 0 \\ x^3 + cx^2 + ax + b =0 \end{cases}}\]

Calvin and Brian play the following game. At the beginning, Calvin choose a number \(a\), then Brian chooses a number \(b\), and then Calvin chooses a number \(c\). Can Calvin choose his numbers in such a way that the three equations listed above have a common:

\((A)\) real root?
\((B)\) negative root?


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