Find the multiplicity of each zero of the function.
f(x) = (x+3)^2(x-4)^3
What is the multiplicity of the zero x= -3
What is the multiplicity of the zero x= 4
I looked at a few multiplicity problems but none of them looked like my problems, so I was just confused.
Do I just plug in the -3 and the 4? Sorry if that's a dumb question, but I just want to be sure.
If anyone can help me start off the problem I would appreciate it.
the power of the factor is the multiplicity of the root -- the number of times the factor appears.
So, -3 has multiplicity 2
4 has multiplicity 3
Ohhhhhhhhhh
so, x+3=0 -> x=-3 and it has a multiplicity 2 since it's to the power of 2
x-4=0 -> x=4 and it has a multiplicity of 3 since it's to the power of 3
Is that correct?
Yeah, the problems I was looking at are totally different, so I just ended up overthinking this. Thank you!
To find the multiplicity of each zero of the function, you need to understand the concept of zero or root multiplicity in polynomial functions. The multiplicity of a zero is the number of times that the factor (x - a) occurs in the factored form of the function.
In this case, the function f(x) = (x+3)^2(x-4)^3 is already factored. The factor (x + 3) appears twice with an exponent of 2, and the factor (x - 4) appears three times with an exponent of 3.
To determine the multiplicity of the zero x = -3, you need to look at the exponent of the factor (x + 3), which is 2. The multiplicity of the zero x = -3 is 2 because the factor occurs twice.
To determine the multiplicity of the zero x = 4, you need to look at the exponent of the factor (x - 4), which is 3. The multiplicity of the zero x = 4 is 3 because the factor occurs three times.
So, to answer your questions directly:
- The multiplicity of the zero x = -3 is 2.
- The multiplicity of the zero x = 4 is 3.
You do not need to plug in the values -3 and 4 to find the multiplicity; you can determine it from the factored form of the function.