A cubic game

Algebra Level 2

Brilli the Ant and Brian Till are at it again. Unlike last time, they are playing the cubic game.

In one move, Brilli is going to choose a real number and Brian puts it in one of the empty spaces in the cubic equation below:

\(x^3 + \underline{\hspace{0.3 cm}} \, x^2 + \underline{\hspace{0.3 cm}} \, x + \underline{\hspace{0.3 cm}} \, = 0\)

After 3 moves, the game is over. Brilli wins the game if the final equation has 3 distinct integer roots.

Who has the winning strategy?


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