Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

angelwings996 Group Title

Find all the zeros of the equation. x^4 - 6x^2 - 7x - 6 = 0

  • one year ago
  • one year ago

  • This Question is Closed
  1. mathmate Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Using Descartes rule of signs, there is one positive root, one or three negative roots.

    • one year ago
  2. angelwings996 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    I'm sorry, I'm so confused. I don't really know what I am suppose to do or use to figure this problem out

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

    The factorization theorem says if there are rational roots, they would be the factors of 6, or you can try factors like (x+1), (x-1), (x-2), (x+2), (x-3),(x+3),(x-6),(x+6). Since it can be shown that x+1 and x-1 are not factors, there are two out of the remaining six are zeroes. Let f(x)=x^4 - 6x^2 - 7x - 6 , you can try f(2)=2^4-6*2^2-7*2-6=16-24-14-6=-28 But since f(-2)=16-24+14-6=0, we conclude that x=-2 is a zero. Continue trying f(3) [because -2*3=-6, the constant term to see if x=3 is a zero.

    • one year ago
  4. angelwings996 Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    Oh I get it. So I am just plugging in numbers 1 - 6 both positive and negative to see which one(s) will equal zero, correct ?

    • one year ago
  5. mathmate Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    Yes, except that you only plug in factors of 6. So you can skip 4 and 5, because 4 and 5 are not factors of 6. This is true when the leading coefficient is 1 (i.e. 1x^4). If the leading coefficient is not 1, then we have to check all combinations of (ax\(\pm b)\), where a is one of the factors of the leading coefficient, and b is one of the factors of the constant term. Thank you for the medal.

    • one year ago
    • Attachments:

See more questions >>>

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.