Results 1 to 3 of 3

Math Help - Math Contest Problem

  1. #1
    Newbie
    Joined
    Feb 2011
    Posts
    13

    Math Contest Problem

    I would really appreciate any help on this problem! It was from the 2002 Luzerne County Math Contest. How many real roots does x^6 - 6x^3 + x^2 - 2x + 11 possess? No calculator is allowed.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    skeeter's Avatar
    Joined
    Jun 2008
    From
    North Texas
    Posts
    11,689
    Thanks
    448
    Quote Originally Posted by eric1299171 View Post
    I would really appreciate any help on this problem! It was from the 2002 Luzerne County Math Contest. How many real roots does x^6 - 6x^3 + x^2 - 2x + 11 possess? No calculator is allowed.
    x^6 - 6x^3 + x^2 - 2x + 11 =

    x^6 - 6x^3 + 9 + x^2 - 2x + 1 + 1 =

    (x^3 - 3)^2 + (x - 1)^2 + 1

    what does the last expression tell you about possible real roots?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2011
    Posts
    13
    There are no real roots since it is always greater than zero. Thanks for the help! =)
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Math Contest Problem 3
    Posted in the Statistics Forum
    Replies: 2
    Last Post: March 20th 2011, 12:43 PM
  2. Math Contest Problem
    Posted in the Algebra Forum
    Replies: 8
    Last Post: February 5th 2011, 07:40 PM
  3. Help for a Math Contest
    Posted in the Math Topics Forum
    Replies: 1
    Last Post: April 15th 2010, 04:08 PM
  4. Math Contest Word problem
    Posted in the Algebra Forum
    Replies: 2
    Last Post: November 12th 2009, 06:38 PM
  5. math contest problem on probability.
    Posted in the Statistics Forum
    Replies: 2
    Last Post: November 12th 2009, 06:25 PM

Search Tags


/mathhelpforum @mathhelpforum