## marcelie one year ago help please how do i find the multiplicity and zeros. i attached a picture.

1. marcelie

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

2. ganeshie8

Have you tried factoring the given polynomial ?

3. marcelie

yes. hold on let me take pic of it .

4. marcelie

5. zepdrix

Oo I like that pen, what is that?

6. ganeshie8

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

7. marcelie

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

8. ganeshie8

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

9. marcelie

okay one sec.

10. ganeshie8

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

11. ganeshie8

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

12. marcelie

|dw:1444371566488:dw|

13. marcelie

|dw:1444371609598:dw|

14. 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 :)

15. marcelie

oh.

16. ganeshie8

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

17. marcelie

its can be +/- ?

18. marcelie

can synthetic be possible too ?

19. marcelie

yes

20. ganeshie8

negative discriminant tells you that the roots are not real

21. marcelie

bc for the 2nd equation i got i's

22. marcelie

lordie... im confuse

23. 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

24. marcelie

yes.

25. marcelie

but my solution book says 3 with multiplicity of 2

26. marcelie

27. 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

28. marcelie

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

29. marcelie

30. marcelie

31. marcelie

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

32. 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.

33. zepdrix

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

34. marcelie

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

35. marcelie

how the hell they get 3 wit multi 4 ?

36. zepdrix

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

37. marcelie

true.. i hate this online book

38. marcelie

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

39. marcelie

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

40. zepdrix

oh you have to graph it now? :o interesting

41. 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.

42. marcelie

i think so lol

43. marcelie

so yall think my book is wrong

44. 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?

45. marcelie

hmmm

46. 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.

47. marcelie

hmm