Question

The graph of f(x) = x2 – 3x2 + 4 is shown

Based on the graph, how many distinct real number
solutions does the equation x3 - 3x2 + 4 = 0 have?

Answer 1

2 is the answer that I would give. The question says distinct solutions does this graph have.

Explanation:

You are asked only how many times this crosses the x axis. You are not asked for an exact value. So the thing to do is graph the polynomial.

y = x^3 - 3x^2 + 4

The graph says that x = -1 with a multiplicity of 1

It also says that x=2 is a solution with a multiplicity of 2 (meaning there are 2 roots are the same).

So this polynomial factors into y = (x + 1)(x - 2)(x - 2)