Question

Find the zeros of the function ,giving the multiplicity *PLEASE HELP* : f(x)=-3(x+1/2)(x-3)^3 ????

Answer 1

Do you know what the zero-product property is?

Answer 2

Not really

Answer 3

Alright here it is. If (x-5)(x-3) = 0 then (x-5) = 0 or (x-3) = 0

Answer 4

Do you think you could do that with the problem you have above?

Answer 5

Ohh

Answer 6

What do you do with the number in front of the parenthesis?

Answer 7

Take each product and set it = to 0

Answer 8

You can set that = to zero but -3≠0 so that won't be a solution

Answer 9

Now set the other two equal to zero.

Answer 10

-1/2 and 3...

Answer 11

Yeah those are your two solutions. But you have to state the multiplicities. Do you know what they are?

Answer 12

No

Answer 13

okay so x+1/2=0, x=-1/2 has a multiplicity of one
and x-3=0 , x=3 has a multiplicity of 3. That's because it was cubed.

Answer 14

Ok

Answer 15

So do you get it now Miranda?

Answer 16

Miranda?

Answer 17

Nevermind.

Answer 18

1 more?

Answer 19

Sure.

Answer 20

F(x)=x^3-2x^2+x

Answer 21

Find zeros?

Answer 22

Yeah

Answer 23

Okay. What can we factor out right now?

Answer 24

What does each term have at least one of

Answer 25

So: x(x^2-2x+1)?

Answer 26

Good.

Answer 27

Now can you factor what's inside the parenthesis?

Answer 28

Yeah

Answer 29

F(x)=x^3-2x^2+x

Answer 30

1 more?

Answer 31

We're not done yet. we have yet to find the zeros.

Answer 32

X=1

Answer 33

No

Answer 34

factor what's inside the parenthesis.

Answer 35

x(x^2-2x+1)?

Answer 36

hint: You'll have x(x-?)(x-?)

Answer 37

I did : (x-1)(x-1), set it equal to 0, its x=1,x=1

Answer 38

Oh okay. Well you didn't tell me you factored it. Yeah that would be right.
So in the end you would have
x(x-1)(x-1) which can be simplified to x(x-1)^2
You told me one zero, what's the other one and also tell me the multiplicities.

Answer 39

1

Answer 40

Okay so you have to make sure you set all the products = to 0
You forgot the x that's standing all alone. so x = 0 or x-1=0

Answer 41

x=0 has a multiplicity of 1 and x=1 has a mutliplicity of 2.
I think you should get the multiplicity thing now. we had (x-1)(x-1) or (x-1)^2
That's two of the same zero, which is the multiplicity.

Answer 42

K,thanks

Answer 43

Are you good now? You're a pretty smart cookie.