marcelie
  • marcelie
help please how do i find the multiplicity and zeros. i attached a picture.
Mathematics
schrodinger
  • schrodinger
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marcelie
  • marcelie
Find all zeros of the following polynomial functions, noting multiplicities. f (x) = 2x^6 − 6x^5 + 18x^4
ganeshie8
  • ganeshie8
Have you tried factoring the given polynomial ?
marcelie
  • marcelie
yes. hold on let me take pic of it .

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marcelie
  • marcelie
1 Attachment
zepdrix
  • zepdrix
Oo I like that pen, what is that?
ganeshie8
  • ganeshie8
Very good! so far, you have figured out that "0" is a zero with a multiplicity of "4"
marcelie
  • 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
  • ganeshie8
ofcourse yes, quadratic formula is always there for quadratic polynomials, use it..
marcelie
  • marcelie
okay one sec.
ganeshie8
  • ganeshie8
but wait a moment, you could also tell a lot about zeroes from the sign of discriminant
ganeshie8
  • ganeshie8
Look at only the quadratic polynomial : \(x^2-3x+9\) whats the value of its discriminant ?
marcelie
  • marcelie
|dw:1444371566488:dw|
marcelie
  • marcelie
|dw:1444371609598:dw|
anonymous
  • 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
  • marcelie
oh.
ganeshie8
  • ganeshie8
discriminant is just -27, what does that tell you about the roots ?
marcelie
  • marcelie
its can be +/- ?
marcelie
  • marcelie
can synthetic be possible too ?
marcelie
  • marcelie
yes
ganeshie8
  • ganeshie8
negative discriminant tells you that the roots are not real
marcelie
  • marcelie
bc for the 2nd equation i got i's
marcelie
  • marcelie
lordie... im confuse
Directrix
  • 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
  • marcelie
yes.
marcelie
  • marcelie
but my solution book says 3 with multiplicity of 2
marcelie
  • marcelie
sumone please help me .. im so lost DX
zepdrix
  • 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
  • marcelie
yes. :( let me show you the problem. please dont leave me hanging lol
marcelie
  • marcelie
marcelie
  • marcelie
1 Attachment
marcelie
  • marcelie
so idk .. if i factored out wrong or the paper is wrong
zepdrix
  • 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
  • zepdrix
I think you're doing something silly, like not looking at the correct answer key or something >.>
marcelie
  • marcelie
z. lol answer is 0 with multiplicity 4, 3 with multiplicity 2
marcelie
  • marcelie
how the hell they get 3 wit multi 4 ?
zepdrix
  • zepdrix
3 with multiplicity 2? I dunno, they're being silly billies. Books make mistakes sometimes.
marcelie
  • marcelie
true.. i hate this online book
marcelie
  • marcelie
so how do i graph it since i have i 's
marcelie
  • marcelie
second equation gives me - as answer so that cant b taken its a neg right ?
zepdrix
  • zepdrix
oh you have to graph it now? :o interesting
Directrix
  • 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
  • marcelie
i think so lol
marcelie
  • marcelie
so yall think my book is wrong
zepdrix
  • 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
  • marcelie
hmmm
Directrix
  • 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
  • marcelie
hmm

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