Results 1 to 2 of 2

Math Help - Roots of a quadratic

  1. #1
    Newbie
    Joined
    Oct 2008
    Posts
    2

    Roots of a quadratic

    Hi all,
    I would appreciate some help on how to solve the following problem.

    If x^2+kx+54=0 has one root that is twice the other root, what are the values of k?

    Thanks a lot!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    earboth's Avatar
    Joined
    Jan 2006
    From
    Germany
    Posts
    5,830
    Thanks
    123
    Quote Originally Posted by asamimasa View Post
    Hi all,
    I would appreciate some help on how to solve the following problem.

    If x^2+kx+54=0 has one root that is twice the other root, what are the values of k?

    Thanks a lot!
    The equation has the solutions:

    x = t~\vee~ x = 2t

    Then

    (x-t)(x-2t)=0~\implies~x^2-3t+2t^2 = 0

    Thus:

    2t^2 = 54  ~\implies~t = 3\sqrt{3}~\vee~t = -3\sqrt{3}

    And therefore

    k = -9\sqrt{3}~\vee~k=9\sqrt{3}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. quadratic roots
    Posted in the Algebra Forum
    Replies: 5
    Last Post: November 27th 2009, 09:45 PM
  2. Roots of a Quadratic equation
    Posted in the Algebra Forum
    Replies: 1
    Last Post: November 5th 2009, 12:34 AM
  3. Quadratic Roots
    Posted in the Algebra Forum
    Replies: 5
    Last Post: December 3rd 2008, 03:56 PM
  4. The roots of a quadratic equation
    Posted in the Math Topics Forum
    Replies: 2
    Last Post: December 1st 2008, 07:50 AM
  5. Roots of a quadratic
    Posted in the Algebra Forum
    Replies: 1
    Last Post: October 24th 2008, 09:46 AM

Search Tags


/mathhelpforum @mathhelpforum