Results 1 to 6 of 6

Math Help - Find the zeros?

  1. #1
    Junior Member
    Joined
    Sep 2009
    Posts
    54

    Find the zeros?

    Find the zeros (if any) of this rational function.
    g(x) = (x^3 - 8) / (x^2 + 1)

    I'm not sure how to solve this. Any tips?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1573
    Awards
    1
    What about x=2?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Sep 2009
    Posts
    54
    How did you get that?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1573
    Awards
    1
    Quote Originally Posted by tsmith View Post
    How did you get that?
    By simple imspection: 2^3-8=0.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Senior Member pacman's Avatar
    Joined
    Jul 2009
    Posts
    448
    factoring it we have,

    g(x) = (x - 2)(x^2 + 2x + 4)/(x^2 + 1),

    @ x = 2; g(x) vanishes ..... this factor (x^2 + 2x + 4) has no real root,

    the discriminant is b^2 - 4ac = 2^2 -4(1)(4) = -12 < 0.

    The graph below confirms it, x = 2 is the only ZERO of the function
    Attached Thumbnails Attached Thumbnails Find the zeros?-frt.gif  
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor
    Joined
    Mar 2007
    Posts
    1,240

    Talking

    Quote Originally Posted by tsmith View Post
    Find the zeros (if any) of this rational function.
    g(x) = (x^3 - 8) / (x^2 + 1)

    I'm not sure how to solve this. Any tips?
    Hint: A fraction is zero when its numerator is zero.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. find Zeros
    Posted in the Trigonometry Forum
    Replies: 2
    Last Post: July 12th 2010, 12:39 PM
  2. find the zeros of...
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: May 18th 2010, 12:55 PM
  3. Find all the Zeros
    Posted in the Pre-Calculus Forum
    Replies: 9
    Last Post: November 14th 2009, 04:45 PM
  4. Find All Zeros
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: September 22nd 2009, 10:54 AM
  5. Find the zeros
    Posted in the Pre-Calculus Forum
    Replies: 8
    Last Post: September 18th 2009, 04:03 PM

Search Tags


/mathhelpforum @mathhelpforum