What are the zeroes of the function? What are their multiplicities?
f (x) = 4x^3 – 20x^2 + 24x (1 point)
The numbers –3, –2, and 0 are zeroes of multiplicity 1.
The numbers 3, 2, and 0 are zeroes of multiplicity 2.
The numbers –3, –2, and 0 are zeroes of multiplicity 2.
The numbers 3, 2, and 0 are zeroes of multiplicity 1.

Question

What are the zeroes of the function?  What are their multiplicities?
f (x) = 4x^3 – 20x^2 + 24x  (1 point)
The numbers –3, –2, and 0 are zeroes of multiplicity 1.
The numbers 3, 2, and 0 are zeroes of multiplicity 2.
The numbers –3, –2, and 0 are zeroes of multiplicity 2.
The numbers 3, 2, and 0 are zeroes of multiplicity 1.

campbell_st · Answer

well factor out 4x first

$$f(x) =4x(x^2 - 5x + 6)$$

now factor the quadratic inside the brackets... 

then determine how mnay times each factor occurs.. 

4x has multipliciy of 1 since it only occurs once

look at the factors of 

$$x^2 - 5x + 6$$ and see how often they occur. 

hope this helps

anonymous · Answer

It didn't help much, sorry. I'm still confused :c

campbell_st · Answer

ok... so the polynomial can be factorised to 

$$f(x) = 4x(x -3)(x-2) $$

so each factor occurs once... so multiplicity is 1

is you had 

$$f(x) = 4x(x - 2)^2  $$

then 4x has multiplicity of 1 and (x-2) has multiplicity of 2 

so now its factored to find the zeros solve

$$0=4x(x-3)(x-2) $$

hope this helps a little

anonymous · Answer

I really have no idea. I don't get this at all. But, if I had to guess, I'd probably say B

anonymous · Answer

I didn't, I'm just guessing.

anonymous · Answer

I know, but I really don't understand it.