A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

Can you help with an explanation can someone tell me if this problem is correct, list the possible rational roots? f(x)=x^2+4x-5 ans: (x-1)(x+5)=x=1 x=-5 +-1,+-4,+-5=/1=+-1,+-4,+-5 ans:{1,-5

  • This Question is Closed
  1. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    if you use the enter key; itll make that alot more readable kind of like doing this so that we can see it clearly rathrthansomeconglomoratedmessthatwehavetodecipher

  2. Yuki
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I asked you if you needed help with the explanation with the rational root theorem

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

    yes i do should i reenter the problem

  4. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yes please

  5. Yuki
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    nope, the problem is not that relevant

  6. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    the manners are tho :)

  7. Yuki
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I will start explaining so pay close attention okay ? i'll go through the idea of the proof so that you can remember it

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

    ok

  9. amistre64
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    yuki; been down this road; but good luck ;)

  10. Yuki
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    If you let any polynomials of form P(x) = 0, you can solve for the roots. where polynomials are generally of the form \[P(x) = {a_n}x^n + a_{n-1}x^{n-1}+ ... + a_1x +a_0\]

  11. Yuki
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    the only thing that really matters here is the leading term and the constant term, so I will abbreviate the middle part as Q now, one of the ways to solve for the root systematically, you take the following steps \[a_n x^n + Q + a_0 = 0\] \[a_n x^n + Q = -a_0 \] \[x^n +Q/a_n = {-a_0 \over a_n}\] the last term is very important

  12. Yuki
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    I won't go into any more details, but if you keep doing this you will eventually come to a conclusion saying, x^n must be some power of a_0 / a_n thus a possible number of x, must be of form p/q where p = all factors of a_0 q = all factors of a_n

  13. Yuki
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    when all coefficients of P(x) are integers

  14. Yuki
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    Therefore, the main idea is this if a polynomial P(x) have coefficients only made of integers, then the possible rational roots are + or - p/q. where p is the factors of the constant, and q is the factors of the leading coefficient.

  15. Yuki
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    in your problem, the constant term is -5 and the factors are + or - 1 and 5. the leading coefficient is 1, so the factors are + or - 1. since you have + or - for both top and bottom, we will ignore that for now and put it later once we find the positive version of the possible rational roots. they have to have the form p/q where \[p = \pm 1, 5 and q = \pm 1\]

  16. Yuki
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    thus \[{p \over q} = \pm 1 , \pm 5\]

  17. Yuki
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    let's say that your leading coefficient was actually, 10, because I want you to see the pattern better. now p is still the same, but q will now be \[\pm 1, 2, 5,10\]

  18. Yuki
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so technically, p/q will now be \[\pm {1 \over 1},{5 \over 1}\] \[\pm {1 \over 2}, {5 \over 2}\] \[\pm {1 \over 5}, {5 \over 5}\] \[\pm {1 \over 10}, {5 \over 10}\] are all of my combinations

  19. Yuki
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    but as you can see, \[\pm {1 \over 1} = \pm {5 \over 5}\] and also \[\pm {1 \over 2} = \pm {5 \over 10}\]

  20. Yuki
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    so we are double counting. once you eliminate those and simplify for a polynomial that looks like \[P(x) = 10x^4 + 3x^2 + x -5\] the possible rational roots are \[{p \over q } = \pm 1,5,1/2,5/2,1/5,1/10\]

  21. Yuki
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    one last thing. the rational root theorem only tells you the "possible" roots so it doesn't mean that one of those are guaranteed to be an actual solution. for example, \[f(x) = x^2 +1\]

  22. Yuki
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    it is obvious that this quadratic has no real roots, but the possible rational roots according to the thm are + or - 1. which both will fail. so always keep in mind that it is just a "fairly good guess"

  23. Yuki
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    does that help ?

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

    yes very much

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

    thank u

  26. Yuki
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 1

    good luck in whatever you need to do :)

  27. 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.