Assume player 2 chooses actions at random with each action having equal probability (and player 1 knows this). for what values of x is player 1 guaranteed to choose action 1?

you are saying it as if a fact, not a question, but yes, you would be correct? ; )

step-by-step explanation:

f(x) = x^3 -2x^2 -3x

x( x^2 -2x-3)

x( x^2 +x -3x -3)

x( x(x+1) -3(x+1))

x( x-3)( x+1)

so zeroes are 0, 3,-1

its (2) option