find the zeroes and state the multiplicity of multiple zeroes
y=(x+1)^2 (x-1) (x-2)
I know that
x=-1
x=1
x=2
I don't know how to find the multiplicities
technicality here
from (x+1)^2
we have (x+1)(x+1)
so x = -1 or x = -1
same root shows up twice, so they call it a multiplicity of 2
your zeros are correct
To find the multiplicity of each zero in the given equation, we need to determine how many times each factor appears in the equation. Multiplicity refers to the number of times a particular factor is repeated.
Looking at the equation, y = (x+1)^2 (x-1) (x-2), we can see that:
1. (x+1) is a factor with a multiplicity of 2. This means that (x+1) appears twice as a factor. We can write it as (x+1)^2.
2. (x-1) is a factor with a multiplicity of 1. It appears only once in the equation.
3. (x-2) is a factor with a multiplicity of 1. It also appears only once.
Therefore, the zeroes and their multiplicities are:
Zero at x = -1 with multiplicity 2
Zero at x = 1 with multiplicity 1
Zero at x = 2 with multiplicity 1