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Posers and Puzzles

Posers and Puzzles

  1. 03 Nov '08 05:07 / 2 edits
    I have this math problem that I am stuck on. You have to find f(x) if the roots are x=(1/7), -6+3i, -6-3i, ((-5+sqrt(7))/(2)), and ((-5-sqrt(7))/(2)), and the y-intercept is (0,-162) and f(-5) does not exist. You also have to find the oblique asymptote and explain why f(-5) does not not exist. I think that I found the correct function: f(x)=5.6x^5-40x^4-53.2x^3+966x^2+997.2x-162, but I don't know how to find the oblique asymptote, or why f(-5) does not exist. I have probably been very confusing in wording this problem, but I did the best I could. Would any of you guys happen to know how to find the oblique asymptote or why f(-5) does not exist? Any help would be greatly appreciated.
  2. Standard member ChronicLeaky
    Don't Fear Me
    03 Nov '08 05:38
    Originally posted by UserChevy
    I have this math problem that I am stuck on. You have to find f(x) if the roots are x=(1/7), -6+3i, -6-3i, ((-5+sqrt(7))/(2)), and ((-5-sqrt(7))/(2)), and the y-intercept is (0,-162) and f(-5) does not exist. You also have to find the oblique asymptote and explain why f(-5) does not not exist. I think that I found the correct function: f(x)=5.6x^5-40 ...[text shortened]... find the oblique asymptote or why f(-5) does not exist? Any help would be greatly appreciated.
    Without specifying some other attributes of f, there are uncountably many answers.
  3. 03 Nov '08 08:28
    Originally posted by UserChevy
    I have this math problem that I am stuck on. You have to find f(x) if the roots are x=(1/7), -6+3i, -6-3i, ((-5+sqrt(7))/(2)), and ((-5-sqrt(7))/(2)), and the y-intercept is (0,-162) and f(-5) does not exist. You also have to find the oblique asymptote and explain why f(-5) does not not exist. I think that I found the correct function: f(x)=5.6x^5-40 ...[text shortened]... find the oblique asymptote or why f(-5) does not exist? Any help would be greatly appreciated.
    i think the equation you are looking for can be found from a few steps:

    1. let the product of all the roots = g(x) (ex. (7x-1)(x^2+6x+15)(4x^2+20x+18) = g(x) )
    in other words, let each of the roots = zero, rearrange to put all the terms on one side (i.e. x=1/7 becomes 7x-1=0) and then using the reverse of the zero-product rule, you can find a polynomial that gives you zero.

    now, for this equation, g(0) = -270 which is not -162. so you have to multiply through by a constant multiplier, in this case let f(x) = 162/270 * g(x). now we have the first two parts in order.

    for f(-5) not to exist, the denominator must -> 0 as x->-5, in other words, put an (x+5) in the denominator.

    and as far as an oblique asymptote goes, there are a number of possible answers. if there is only an (x+5)^1 power in the denominator, then there's no asymptote so the function rises to infinity. if there is a higher degree (for example (x+5)^15 ) in the denominator, then as x moves toward positive infinity, a horizontal asymptote of y=0 appears.

    however, if the degree in the numerator is one greater than the degree of the denominator (our roots give us a 5th degree polynomial beginning with 28x^5) an oblique asymptote will be apparent as x approaches infinity. so... let the denominator be (x+5)^4, and do a little polynomial division. you will get a linear term and a fraction that goes to zero. so the oblique asymptote will be y = (linear term of the division)

    i hope this helps i'm just too lazy to do the actual work for the last part and hopefully you'll know follow what i'm trying to say
  4. 03 Nov '08 15:15
    Originally posted by Aetherael
    i think the equation you are looking for can be found from a few steps:

    1. let the product of all the roots = g(x) (ex. (7x-1)(x^2+6x+15)(4x^2+20x+18) = g(x) )
    in other words, let each of the roots = zero, rearrange to put all the terms on one side (i.e. x=1/7 becomes 7x-1=0) and then using the reverse of the zero-product rule, you can find a polyno ...[text shortened]... do the actual work for the last part and hopefully you'll know follow what i'm trying to say
    Am I nerdy to like this posting? I loved it!
  5. Subscriber joe shmo On Vacation
    Strange Egg
    03 Nov '08 19:34
    Originally posted by FabianFnas
    Am I nerdy to like this posting? I loved it!
    yes you are nerdy, but you are in company, because I enjoyed it as well..
  6. 04 Nov '08 04:59 / 1 edit
    Originally posted by Aetherael
    i think the equation you are looking for can be found from a few steps:

    1. let the product of all the roots = g(x) (ex. (7x-1)(x^2+6x+15)(4x^2+20x+18) = g(x) )
    in other words, let each of the roots = zero, rearrange to put all the terms on one side (i.e. x=1/7 becomes 7x-1=0) and then using the reverse of the zero-product rule, you can find a polyno do the actual work for the last part and hopefully you'll know follow what i'm trying to say
    This was a very helpful post, thanks for helping out. I still think that I might have messed up the oblique asymptote, as I got a 5th degree polynomial for the oblique asymptote, but it is supposed to be a 4th degree polynomial? Oh well, I think that I got the right function anyways, and thank you for your post.
  7. 05 Nov '08 10:51
    you're welcome it makes me happy to have people enjoy my self-proclaimed nerdy math posts haha. i used to love posting in this posers/puzzles forum but haven't been here in a long time. you guys have brought me back