The root [tex]x=-3[/tex] has multiplicity one and the root [tex]x=4[/tex] has multiplicity two.
Explanation:
Given that the function [tex]f(x)=(x+3)(x-4)^2[/tex]
We need to determine the multiplicity of the function.
The function has 2 roots.
The roots of the function are -3 and 4.
The multiplicity of the roots means the number of times the root is a factor of the polynomial.
Thus, from the function, it is obvious that the function has the root -3 which occurs exactly once.
Thus, the root [tex]x=-3[/tex] has multiplicity one.
Also, the root of the function [tex]x=4[/tex] which occurs twice.
Thus, the root [tex]x=4[/tex] has multiplicity two.
Hence, the multiplicity of the function is the root [tex]x=-3[/tex] has multiplicity one and the root [tex]x=4[/tex] has multiplicity two.
