A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • one year ago

Descartes' Rule of Signs: 2x^4-7x^3+3x^2+8x-4 This equation shows that there would be either 3 positive roots, or 1 positive root, but my answer and the answer at the back of my textbook say that there are only two positive roots; 1/2, and 2. The Descartes' Rule of Signs says that the number of positive roots is either equal to the number of variations in sign or is less than that by an even whole number. Why does that not apply to this equation?

  • This Question is Closed
  1. amistre64
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    what are the number of variations in your positive setup?

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

    I was thinking that it was 3 variations

  3. amistre64
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    2x^4 -7x^3 +3x^2 +8x -4 | | | 0 1 2 3 i count 3 as well

  4. amistre64
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    do you recall that a root can be repeated right?

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

    I was thinking about that also, but why would we have to subtract the number of variations by 2, instead of 1, if we were accounting for repeats?

  6. amistre64
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    the subtraction by 2 is to account for complex (nonreal) roots which always come in conjugate pairs

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

    I see. What would we do about the repeating roots, then?

  8. amistre64
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    repeating roots was just a thought, but it has 3 postivie roots http://www.wolframalpha.com/input/?i=0%3D2x^4-7x^3%2B3x^2%2B8x-4

  9. amistre64
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    does the question ask you to find the roots? or just the number of them?

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

    It asks to find all the real roots.

  11. amistre64
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    and you are sure that your looking up the right answer key with the right question? also, books do have errors in them

  12. amistre64
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    attaching a picture might help verify your cause :)

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

    Yep, it has the roots 1/2, 2, and -1. Doesn't the graph in the link have two positive roots and one negative root? :o

  14. amistre64
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    i am so glad you are on top of these things ... so yeah, there is a double root. so, it has 3 positive roots. 1/2, 2, 2 it is just that one of them occurs more than once.

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

    Okays, so when solving these kinds of problems, we should assume there is a double root if the answer isn't the correct number of variations?

  16. amistre64
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    you discover it either by working out the division ... or by the graph

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

    I see. Graphing...

  18. amistre64
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    as long as no errors occur in print, yeah, you can assume that one or more of the roots are a multiple root if we count 3 or 1, and only find '2' of them.

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

    Great, thanks!

  20. amistre64
    • one year ago
    Best Response
    You've already chosen the best response.
    Medals 1

    your welcome

  21. 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.