Game of Equations!

Algebra Level 5

{x3+ax2+bx+c=0x3+bx2+cx+a=0x3+cx2+ax+b=0\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 aa, then Brian chooses a number bb, and then Calvin chooses a number cc. Can Calvin choose his numbers in such a way that the three equations listed above have a common:

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


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