Results 1 to 4 of 4
Like Tree3Thanks
  • 1 Post By HallsofIvy
  • 2 Post By johnsomeone

Math Help - product of roots

  1. #1
    Member
    Joined
    Nov 2010
    Posts
    112

    product of roots

    let P(x)=0 be a polynomial equation of least possible degree with rational coefficients having \sqrt[3]7+\sqrt[3]49 as one of its roots
    .then the product of all the roots of P(x)=0 is
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    16,241
    Thanks
    1795

    Re: product of roots

    You left out an awful lot of information. What kind of course did you see this problem in? What do you know about such problems? What ideas do you have about it? Do you have, for example, a "guess" as to what degree this polynomial should be?
    Thanks from ayushdadhwal
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Sep 2012
    From
    Washington DC USA
    Posts
    525
    Thanks
    147

    Re: product of roots

    Let a = 7^{\frac{1}{3}}. Let b = a + a^2.

    Note a^3 = 7, which will be used to simplify powers of a greater than 2.

    b^3 = (a + a^2)^3 = (a)^3(1+a)^3 = 7(a^3 + 3a^2 + 3a + 1) = 7(7 + 3a^2 + 3a + 1)

    = 21a^2 + 21a + 56 = 21(a^2 + a) + 56 = 21b + 56.

    Can you complete it from here?
    Thanks from HallsofIvy and ayushdadhwal
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Member
    Joined
    Nov 2010
    Posts
    112

    Re: product of roots

    sir this is the exact wording given in book.one thing i am sure that they are working on real field.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. sum and product of roots
    Posted in the Algebra Forum
    Replies: 3
    Last Post: July 12th 2011, 11:26 AM
  2. Replies: 5
    Last Post: February 5th 2011, 07:23 AM
  3. Product + Sum of the Roots
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: January 22nd 2010, 05:44 PM
  4. Product & Sum of Roots
    Posted in the Pre-Calculus Forum
    Replies: 2
    Last Post: November 28th 2008, 06:52 PM
  5. Sum and Product of roots ><
    Posted in the Algebra Forum
    Replies: 16
    Last Post: April 7th 2008, 04:18 AM

Search Tags


/mathhelpforum @mathhelpforum