For k = 3 because the curve hits it once. We need 2 more solutions. Which the curve does not show because they are not real rather complex.
I'd say k = 3
then we would have:
However, the graph of will cut the -axis at in one place. Since it is a cubic polynomial, we should get 3 roots, since we would have only 1 real root if we shift the graph 3 units down, the other two roots will be complex
EDIT: Beaten yet again!