Question

F(x) = x3 - 3x2 + 4 = 0 For the equation given, 2 has a multiplicity of? 1, 2, 3

Answer 1

3 It's the highest power.

Answer 2

Multiplicity is how many times
a certain solution to the function.
In this case, we are finding out how many times 2 appears in the function, meaning you’ll have to solve for it when it equals 0. You may use a calculator or use the rational roots method. I will simply derive the answer from the calculator. If you’d like to know about the rational roots method, comment.

x^3 - 3x^2 + 4 = 0 // Given
0 = (x + 1)(x - 2)(x - 2) // Calculator skills
0 = (x + 1)(x - 2)^2 // Simplify

Therefore, 2 has a multiplicity of 2