Question

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

Answer 1

Answer:

See explanation

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.