A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

How could you use Descartes' rule and the Fundamental Theorem of Algebra to predict the number of complex roots to a polynomial as well as find the number of possible positive and negative real roots to a polynomial?

  • This Question is Closed
  1. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    What is Descartes' rule?

  2. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    possible number of the positive roots of a polynomial is equal to the number of sign changes in the coefficients of the terms or less than the sign changes by a multiple of 2.

  3. LynFran
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    http://www.algebra.com/algebra/homework/complex/Complex_Numbers.faq.question.764641.html

  4. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    You don't understand it, right?

  5. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I don't.

  6. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    let's look at example: \(x^5-x^4+x+2=0\) how many time the sign of the term change?

  7. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok!! what is the sign of x^5?

  8. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    + or - ??

  9. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    positive

  10. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    what is the sign of x^4 ?

  11. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    - lol

  12. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes, so, if you go from x^5 to x^4 the sign changes from + to -, right? one time!!

  13. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    now, next , what is the sign of x ?

  14. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Got it! Basically the number of signs changes is the number of possible roots, correct?

  15. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    +

  16. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    possible of REAL ROOT

  17. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    OK, tell me, on the expression above, how many time the sign change in total?

  18. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    2

  19. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yup, so the POSSIBLE real roots are ???

  20. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    2 :)

  21. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    or 0

  22. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    So this is the Descartes rule?

  23. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    YUp

  24. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    How come it's either 0?

  25. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    that is the rule, if the number of the changing of the sign is 6, then the number of real root can be 6,4,2,0

  26. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    multiple of 2, right?

  27. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yup

  28. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    and the complex root:

  29. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    What is the degree of the expression above?

  30. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    5

  31. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yup, so the number of real root are 2 (maximum), hence the maximum of complex is ??

  32. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Are we now talking about the Fundamental Theorem of Algebra?

  33. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yup

  34. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Okay. :) So in the Fundamental Theorem of Algebra, it's about the complex numbers?

  35. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    complex roots, yes

  36. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    roots, I meant. :)

  37. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    ok, how many??

  38. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Okay, so the equation above has a degree of 5.

  39. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yup

  40. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    i already answered that lol

  41. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    degree 5--> maximum 5 roots, we already know that it MAY have 2 real roots, hence, how many complex left?

  42. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    and 2 complex roots, since the real roots are 2

  43. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    perfect!! but confirm: why 2 but 3??

  44. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    because complex roots are always in pairs?

  45. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    idk haha

  46. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yyyyyyyyyyyyyyyyyyyyyyyyyyyyyes!

  47. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    You got it.

  48. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    oh really?

  49. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ok so what now?

  50. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    go to bed!! we are done.

  51. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    That's it?

  52. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    yes, dat sit.

  53. anonymous
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 0

    wow, i didn't know that that's easy. thank you @Loser66 ! :) You're a great help!

  54. Loser66
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    np

  55. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.