The graph of f(x) = x3 – 3x2 + 4 is shown. based on the graph, how many distinct real number solutions does the equation x3 – 3x2 + 4 = 0 have? no real number solution one real number solution two real number solutions three real number solutions

There are two real number solutions.
The number of real solutions is shown by the number of times the graph intersects the x-axis. The graph of f(x) = x^3 - 3x^2 + 4 passes through x = -1, and bounces off x = 2. This means that x = -1 is a solution, and x = 2 is also a solution (of multiplicity 2).