Results 1 to 4 of 4
Like Tree3Thanks
  • 2 Post By Prove It
  • 1 Post By Prove It

Math Help - Determining k so that there is a hole.

  1. #1
    Junior Member
    Joined
    Apr 2012
    From
    Seattle, Washington
    Posts
    72

    Determining k so that there is a hole.

    I've been staring at this problem for a while. I would appreciate a nudge in the right direction.

    Determine k so that f(x)=x^3+kx-4/x-1 has a hole at x=1.

    Here's what I've been able to figure out. In order for there to be a hole at x=1 there has to be a (x-1) in the numerator, right? But I'm not sure how to go about determining k to get (x-1) on top.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,802
    Thanks
    1576

    Re: Determining k so that there is a hole.

    Some brackets would be nice. Assuming you meant f(x) = (x^3 + kx - 4)/(x - 1), you are correct that you need a factor of (x - 1) in the numerator.

    Now remember that by the remainder and factor theorems, that for (x - a) to be a factor of a polynomial P(x), then P(a) = 0. Since you need x - 1 to be a factor, substitute x = 1 into the numerator and equate it to 0. You should be able to find k then.
    Thanks from MarkFL and FatimaA
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Apr 2012
    From
    Seattle, Washington
    Posts
    72

    Re: Determining k so that there is a hole.

    0 = (1)^3 + k(1) - 4

    0 = 1 + k - 4

    0 = -3 + k

    3 = k

    So f(x) = (x^3+3x-4)/(x-1)
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,802
    Thanks
    1576

    Re: Determining k so that there is a hole.

    Correct
    Thanks from FatimaA
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Pigeon-Hole Principle
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: July 30th 2011, 03:48 AM
  2. Pigeon Hole Principle
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: April 11th 2010, 04:27 AM
  3. Replies: 5
    Last Post: February 3rd 2010, 08:14 AM
  4. can someone poke a hole in this?
    Posted in the Calculus Forum
    Replies: 2
    Last Post: March 26th 2009, 08:19 PM
  5. pigeon-hole
    Posted in the Discrete Math Forum
    Replies: 7
    Last Post: December 11th 2008, 02:41 PM

Search Tags


/mathhelpforum @mathhelpforum