Question

The graph of f(x) = x3 – 6x2 + 9x is shown.


Based on the graph, what are the solutions of the equation
x3 – 6x2 + 9x = 0?

x = 3
x = –3, 0
x = 0, 3
x = –3, 0, 3

Answer 1

Factor: x^3 − 6x^2 + 9x = x(x^2 − 6x + 9) = x(x − 3)^2, so the solutions are x = 0 and x = 3 (with x = 3 a double root). Hence the correct choice is: x = 0, 3.