Question

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

Answer 1

two real number solutions

Explanation:

Answer 2

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).