A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

how to find the zeros of \[x ^{3}\] + x + 10

  • This Question is Closed
  1. nikvist
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    \[x^3+x+10=0\] \[(x+2)\cdot(x^2-2x+5)=0\] \[(x+2)\cdot((x-1)^2+4)=0\] \[x_1=-2\quad,\quad x_{2,3}=1\pm 2i\]

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

    but how to find the first step?

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

    well i see - something you have to get used to ^^ thanks a lot

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

    Neasd, you can use the 'rational root theorem' to test for rational roots.

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

    The roots will be of the form\[\frac{p}{q}=\frac{\pm \left\{ factors.of.constant.term \right\}}{\left\{ factors.of.coefficient .of.highest.power \right\}}\]

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

    So here,\[\frac{p}{q}=\frac{\pm \left\{ 1,2,5,10 \right\}}{\left\{ 1 \right\}}\]

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

    \[x=\frac{p}{q}=\frac{-2}{1}=-2\]is one element of the set. When you test this, you find\[(-2)^3+(-2)+10=-8-2+10=0\]so x=-2 is a root. You can then factor \[(x-(-2))=(x+2)\]out of your polynomial.

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

    Do you know how to use long division on polynomials? That is the next step.

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

    long division? hm never heard of that

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

    The aim is to find Q(x) such that\[x^3+x+10=(x+2)Q(x)\]

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

    It's a little difficult to explain on this site. I'll see if I can find a clip that will show you.

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

    a i see polynomdivision ;D my first language is german ^^

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

    yeah i know to do that :D thank you!!

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

    ah, okay :)

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

    The division will find the Q(x), which is the quadratic Nikvist found.

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

    kk thx lucas :)

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

    You're welcome, Markus :)

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

    Just want to add, if you test all the possible rational combinations and none of them satisfy the condition of a root (i.e. your polynomial does not go to zero), the polynomial has *no* rational roots (you're then left with irrational or complex).

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

    ok now i'm prepared :D thx again ;)

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

    np ;)

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

    may i ask you, what you are doing atm? student? postdoc etc? :D

  22. 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.