Answer:
See explanation
Explanation:
The multiplicity of a root of a polynomial equation is the number of times the root repeats.
Let [tex]x=a[/tex] be the root of [tex]f(x)[/tex], then;
[tex](x-a)^1=0[/tex] has a multiplicity of 1.
[tex](x-a)^2=0[/tex] has a multiplicity of 2.
[tex](x-a)^3=0[/tex] has a multiplicity of 3.
[tex](x-a)^m=0[/tex] has a multiplicity of m, where m is a positive integer.
We were given the root [tex]x=-4[/tex].
If [tex]f(x)=(x+4)(x-6)^3[/tex]
Then the multiplicity of the root [tex]x=-4[/tex] is 1.
If [tex]f(x)=(x+4)^4(x-6)^3[/tex]
Then the multiplicity of the root [tex]x=-4[/tex] 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.
