Results 1 to 4 of 4

Math Help - Theory of equation

  1. #1
    Senior Member Sambit's Avatar
    Joined
    Oct 2010
    Posts
    355

    Question Theory of equation

    The problem is to show that the equation (x-1)^3+(x-2)^3+(x-3)^3+(x-4)^3=0 has only 1 real root.

    After simplification, the equation comes out to be of the form ax^3-bx^2+cx-d=0. Applying Descarte's rule of sign we get that the number of +ve real root is 1 or 3, and there is no -ve real root. How can we say then that the number of real root is exactly 1?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Newbie
    Joined
    Jan 2011
    Posts
    15
    Quote Originally Posted by Sambit View Post
    The problem is to show that the equation (x-1)^3+(x-2)^3+(x-3)^3+(x-4)^3=0 has only 1 real root.

    After simplification, the equation comes out to be of the form ax^3-bx^2+cx-d=0. Applying Descarte's rule of sign we get that the number of +ve real root is 1 or 3, and there is no -ve real root. How can we say then that the number of real root is exactly 1?


    f '(x) is always positive, so the graph of the function always raises, it means we have only one real root.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1574
    Awards
    1
    Quote Originally Posted by ahaok View Post
    f '(x) is always positive, so the graph of the function always raises, it means we have only one real root.
    That answer is of course correct, but in this case not useful.
    This is a pre-university pre-algebra/algebra forum.
    So if the question is correctly placed, then derivatives are not used.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member Sambit's Avatar
    Joined
    Oct 2010
    Posts
    355
    Quote Originally Posted by Plato View Post
    That answer is of course correct, but in this case not useful.
    This is a pre-university pre-algebra/algebra forum.
    So if the question is correctly placed, then derivatives are not used.
    That's no problem. I know calculus. I posted the question here since it concerns algebra.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Optimal Control Theory: About the Riccati Dfiferential Equation
    Posted in the Advanced Applied Math Forum
    Replies: 2
    Last Post: June 28th 2010, 12:04 PM
  2. Group Theory - Sylow Theory and simple groups
    Posted in the Advanced Algebra Forum
    Replies: 16
    Last Post: May 16th 2009, 11:10 AM
  3. Number Theory - Primes and Eulers equation
    Posted in the Number Theory Forum
    Replies: 5
    Last Post: August 9th 2007, 11:39 AM
  4. number theory, solve diophantine equation
    Posted in the Number Theory Forum
    Replies: 3
    Last Post: December 3rd 2006, 07:39 PM
  5. Differencial Equation Theory Question
    Posted in the Calculus Forum
    Replies: 5
    Last Post: October 15th 2006, 07:26 PM

/mathhelpforum @mathhelpforum