Question

Consider P(x) = x4(x − 2)3(x + 1)2. What are the zeros of the function? What is the multiplicity of each zero?

Answer 1

A) 0, multiplicity of 4; 2, multiplicity of 3; −1, multiplicity of 2

Explanation:

To find the zeros:

Set each factor equal to zero and solve for x. The zeros are 0, 2, and −1.

The exponent for each factor tells the multiplicity of the zero.

`x^(4)`, 0 has a multiplicity of 4

`(x-2)^3`, 2 has a multiplicity of 3

`(x+1)^2`, −1 has a multiplicity of 2

Answer 2

ifthe roots are r1 and r2
then the factored form is
a(x-r1)(x-r2)
so

and multpilcty is how many times the root repeats
P(x)=(x-0)^4(x-2)^3(x-(-1))^2

so the roots are 0 multipilcty 4, 2 mupliticty 3, -1 multplity 2