help please how do i find the multiplicity and zeros. i attached a picture.

- marcelie

help please how do i find the multiplicity and zeros. i attached a picture.

- schrodinger

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- marcelie

Find all zeros of the following polynomial functions, noting
multiplicities.
f (x) = 2x^6 − 6x^5 + 18x^4

- ganeshie8

Have you tried factoring the given polynomial ?

- marcelie

yes. hold on let me take pic of it .

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## More answers

- marcelie

##### 1 Attachment

- zepdrix

Oo I like that pen, what is that?

- ganeshie8

Very good!
so far, you have figured out that "0" is a zero with a multiplicity of "4"

- marcelie

yes. so im having trouble doing the other one
so do i do the quadratic formula ? bc its going to give me i

- ganeshie8

ofcourse yes, quadratic formula is always there for quadratic polynomials, use it..

- marcelie

okay one sec.

- ganeshie8

but wait a moment, you could also tell a lot about zeroes from the sign of discriminant

- ganeshie8

Look at only the quadratic polynomial : \(x^2-3x+9\)
whats the value of its discriminant ?

- marcelie

|dw:1444371566488:dw|

- marcelie

|dw:1444371609598:dw|

- anonymous

this is easy if you know how to use synthetic division after you find a factor of the equation. Just giving you a side note :)

- marcelie

oh.

- ganeshie8

discriminant is just -27,
what does that tell you about the roots ?

- marcelie

its can be +/- ?

- marcelie

can synthetic be possible too ?

- marcelie

yes

- ganeshie8

negative discriminant tells you that the roots are not real

- marcelie

bc for the 2nd equation i got i's

- marcelie

lordie... im confuse

- Directrix

I'm thinking:
0 is a root of multiplicity 4
3/2 - ( (3i * sqrt(3) ) /2 is a root of multiplicity 1
3/2 + ( (3i * sqrt(3) ) /2 is a root of multiplicity 1

- marcelie

yes.

- marcelie

but my solution book says 3 with multiplicity of 2

- marcelie

sumone please help me .. im so lost DX

- zepdrix

If 3 multiplicity of 2,
then the original equation should have been
\(\large\rm 2x^6-\color{red}{12}x^5+18x^4\)
Are you sure you wrote it down correctly? :o

- marcelie

yes. :( let me show you the problem. please dont leave me hanging lol

- marcelie

##### 1 Attachment

- marcelie

##### 1 Attachment

- marcelie

so idk .. if i factored out wrong or the paper is wrong

- zepdrix

ya your work looks fine :o
https://www.wolframalpha.com/input/?i=roots+of+2x%5E6-6x%5E5%2B18x%5E4
wolfram confirms the roots also.

- zepdrix

I think you're doing something silly,
like not looking at the correct answer key or something >.>

- marcelie

z. lol answer is 0 with multiplicity 4, 3 with multiplicity 2

- marcelie

how the hell they get 3 wit multi 4 ?

- zepdrix

3 with multiplicity 2?
I dunno, they're being silly billies.
Books make mistakes sometimes.

- marcelie

true.. i hate this online book

- marcelie

so how do i graph it since i have i 's

- marcelie

second equation gives me - as answer so that cant b taken its a neg right ?

- zepdrix

oh you have to graph it now? :o interesting

- Directrix

@zepdrix posted the graph as part of the Wolfram work
https://www.wolframalpha.com/input/?i=roots+of+2x^6-6x^5%2B18x^4
It looks like a flat nose parabola but the graph is not a parabola. More of a U-shape.

- marcelie

i think so lol

- marcelie

so yall think my book is wrong

- zepdrix

ya, definitely :o
they made a typo in the function, it shoulda been 12 on the x^5.
It looks like they wanted you to determine the multiplicity based on the graph,
not based on factoring, isn't that what it says? :D
so maybe use a graphing calculator?

- marcelie

hmmm

- Directrix

Yes, I do. E-mail the teacher to discuss it. You should not lose points because of someone's typo and lack of proof reading skills.

- marcelie

hmm

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