Results 1 to 3 of 3

Math Help - Polynomial

  1. #1
    Senior Member Sampras's Avatar
    Joined
    May 2009
    Posts
    301

    Polynomial

    Suppose  p(x) = a_0 + a_{1}x + \cdots + a_{m}x^m . Define  \Gamma(p(x)) = a_{0}^{2}+ a_{1}^{2} + \cdots + a_{m}^{2} . Find a polynomial  g(x) , such that  g(0) = 0 and  \Gamma(p(x)^{n}) = \Gamma(g(x)^{n}) .

    This would be a guess and check process?  \Gamma(p(x)) gives the "distance-squared" from the m-tuple  (a_0, \dots, a_m) to  (0, \dots, 0) .
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by Sampras View Post
    Suppose  p(x) = a_0 + a_{1}x + \cdots + a_{m}x^m . Define  \Gamma(p(x)) = a_{0}^{2}+ a_{1}^{2} + \cdots + a_{m}^{2} . Find a polynomial  g(x) , such that  g(0) = 0 and  \Gamma(p(x)^{n}) = \Gamma(g(x)^{n}) .

    This would be a guess and check process?  \Gamma(p(x)) gives the "distance-squared" from the m-tuple  (a_0, \dots, a_m) to  (0, \dots, 0) .

    g(x)=a_0x+a_1x^2+....+a_nx^{n+1}

    Tonio
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member Sampras's Avatar
    Joined
    May 2009
    Posts
    301
    Quote Originally Posted by tonio View Post
    g(x)=a_0x+a_1x^2+....+a_nx^{n+1}

    Tonio
    Should have been  g(0) = 1 .
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: October 23rd 2011, 06:36 AM
  2. Replies: 1
    Last Post: February 24th 2011, 06:46 PM
  3. Replies: 1
    Last Post: December 15th 2009, 07:26 AM
  4. [SOLVED] dividing polynomial by a polynomial
    Posted in the Algebra Forum
    Replies: 1
    Last Post: February 3rd 2008, 02:00 PM
  5. dividing a polynomial by a polynomial
    Posted in the Algebra Forum
    Replies: 1
    Last Post: August 2nd 2005, 12:26 AM

Search Tags


/mathhelpforum @mathhelpforum