Question

What is the multiplicity of the root x = -4?

Answer 1

See explanation

Step-by-step explanation:

The multiplicity of a root of a polynomial equation is the number of times the root repeats.

Let
`x=a` be the root of
`f(x)`, then;

`(x-a)^1=0` has a multiplicity of 1.

`(x-a)^2=0` has a multiplicity of 2.

`(x-a)^3=0` has a multiplicity of 3.

`(x-a)^m=0` has a multiplicity of m, where m is a positive integer.

We were given the root
`x=-4`.

If
`f(x)=(x+4)(x-6)^3`

Then the multiplicity of the root
`x=-4` is 1.

If
`f(x)=(x+4)^4(x-6)^3`

Then the multiplicity of the root
`x=-4` is 4.

Since the polynomial function or equation is not given in the question, we cannot determine the multiplicity of this root.

But I hope with this explanation, you can refer to the original(complete) question and choose the correct answer.