Question

Consider the function f(x)=(x-3)^2(x+2)^2(x-1).

The zero _____ has a multiplicity of 1.
The zero -2 had a multiplicity of _____

Answer 1

See below in bold.

Explanation:

Because one factor is (x + 1), the zero -1 has a multiplicity of 1.

The zero -2 has a multiplicity of 2 because the factor is (x + 2)^2.

Answer 2

For this case we have that by definition, the multiplicity of the root of a polynomial is given by the number of times the root is repeated. Example:

`(x-1) ^ n`

The zero "1" has a multiplicity of "n".

In this case we have the following function:

`f (x) = (x-3) ^ 2 * (x + 2) ^ 2 * (x-1)`

So:

The zero "3" has a multiplicity of "2".

The zero "-2" has a multiplicity of "2".

The zero "1" has a multiplicity of "1".

Answer:

The zero "1" has a multiplicity of "1".

The zero "-2" has a multiplicity of "2".