Question

What is the multiple zero and multiplicity of f(x) = x³ - 10x² + 25x?

1) multiple zero = 2; multiplicity = -5
2) multiple zero = -5; multiplicity = 2
3) multiple zero = 5; multiplicity = 2
4) multiple zero = 2; multiplicity = 5

Answer 1

The multiple zero of f(x) = x³ - 10x² + 25x is 0 with a multiplicity of 1, and 5 with a multiplicity of 2.

Step-by-step explanation:

The given function is f(x) = x³ - 10x² + 25x. To find the multiple zero and multiplicity, we need to find the values of x that make the function equal to zero.

We can factor out x from the equation: x(x² - 10x + 25) = 0.

This equation has a multiple zero of x = 0 with a multiplicity of 1, and a multiple zero of x = 5 with a multiplicity of 2.