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evy15

Find the roots of the polynomial eq. x^3-3x^2-5x-15=0

  • one year ago
  • one year ago

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  1. mathmate
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    Are you familiar with Descarte's rule of signs?

    • one year ago
  2. mathmate
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    Using Descartes rule of signs, we know that there is one positive real root, and either two negative real roots, or two complex roots.

    • one year ago
  3. evy15
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    no ive neve used it

    • one year ago
  4. evy15
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    never

    • one year ago
  5. mathmate
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    What have you been using to calculate the root of a polynomial equation that does not have rational roots? There is one more thing you could do, double-check the question. This polynomial does not have rational roots.

    • one year ago
  6. dpaInc
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    maybe a numerical method to find the roots?

    • one year ago
  7. mathmate
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    I agree,... if the question had been correctly posted.

    • one year ago
  8. dpaInc
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    or graphing calculator?

    • one year ago
  9. KingGeorge
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    I would go out on a limb, and say that this isn't the correct equation. Some slight sign changes result in an easily factored equation.

    • one year ago
  10. mathmate
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    True, that is for getting an initial estimate.

    • one year ago
  11. mathmate
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    @evy15 we're waiting anxiously your confirmation of the equation!! :)

    • one year ago
  12. dpaInc
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    agree... check that last term... should it really be -15 ???

    • one year ago
  13. evy15
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    yes the equation is correct

    • one year ago
  14. mathmate
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    As @dpalnc said, if the last term is +15, then there are three rational roots (i.e. the equation can be factorized and solved with 3 real rational roots).

    • one year ago
  15. evy15
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    `no its negative

    • one year ago
  16. mathmate
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    In that case, you have 2 complex roots and a real irrational root. What methods have you used so far to solve for irrational roots?

    • one year ago
  17. mathmate
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    Cubics can be solved using Cardano's formula, which is overly complex. We can usually find the real root using a numerical method. Does all this sound familiar to you?

    • one year ago
  18. wio
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    @evy15 Is this homework? Are there certain methods you are supposed to be learning?

    • one year ago
  19. wio
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    Once you find the 1st root, you can use synthetic division an the quadratic equation to find the other two.

    • one year ago
  20. evy15
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    is it -3

    • one year ago
  21. wio
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    The rational root theorem says that it's got to be \[ \pm\frac{1,3,5,15}{1} \]So \(-3\) is a possibility. Try plugging it in.

    • one year ago
  22. KingGeorge
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    Are you absolutely sure that you didn't type it incorrectly? With a small sign change, one of the roots is indeed -3. However, as written, it has one irrational root, and two complex roots.

    • one year ago
  23. evy15
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    the thing is im completely confused because I missed a day in class and now idk how to do it

    • one year ago
  24. evy15
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    its typed in correctly

    • one year ago
  25. joemath314159
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    I checked the solutions to the equation in wolfram, they are pretty intense. If you didnt type the problem incorrectly, then the teacher/professor typed it incorrectly, because there is no way a teacher should expect a student to find those roots by hand =/

    • one year ago
  26. KingGeorge
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    I agree^^

    • one year ago
  27. joemath314159
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    and like others have mentioned, if only one of the signs is changed, it becomes an easy regular standard problem.

    • one year ago
  28. KingGeorge
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    Unless, of course, you're learning about methods to approximate roots.

    • one year ago
  29. joemath314159
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    oh yeah. that could be the case. Newtons Method :)

    • one year ago
  30. evy15
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    its typed correctly

    • one year ago
  31. evy15
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    PLEASE HELP

    • one year ago
  32. dpaInc
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    the only way i can think of if the equation is correct as you say is to approximate the root(s) using newton's method...

    • one year ago
  33. dpaInc
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    or graphing calc. or wolfram.

    • one year ago
  34. evy15
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    on calculator I got -15

    • one year ago
  35. joemath314159
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    If the problem as typed is correct, there is nothing we (or anyone) can do. Not without a calc or comupter, or something.

    • one year ago
  36. dpaInc
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    try to see if x=-15 is a root by plugging that back into the original equation... i don't think that's right.

    • one year ago
  37. dpaInc
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    wait... do you mean to find the y-intercept of \(\large y=x^3-3x^2-5x-15 \) ?? because -15 is the y-intercept...

    • one year ago
  38. joemath314159
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    if thats the actual problem....then lol.

    • one year ago
  39. evy15
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    ok thanks

    • one year ago
  40. dpaInc
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    ho boy...

    • one year ago
  41. mathmate
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    Isn't the question: "Find the roots of the polynomial eq. x^3-3x^2-5x-15=0"

    • one year ago
  42. evy15
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    yes

    • one year ago
  43. mathmate
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    So you need the roots of the equation, not just the y-intercept. As I said in the other post, from the type of question you have, it seems likely that either you or your prof had a typo in this question. To make sure it'd better be your prof, you want to triple check for typos in your post.

    • one year ago
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