Results 1 to 3 of 3

Math Help - quadratic equation

  1. #1
    Member
    Joined
    Apr 2013
    From
    Mahinog
    Posts
    81
    Thanks
    5

    quadratic equation

    Given that the equation x^2 +cx+d=0 and x^2 +3cx+4d=0 have a common root, express d in term of c

    a+b=-c, a+q=-3c
    ab=d aq=4d
    aq-ab=3d
    a(q-b)=3d...(1)
    q-b=-2c...(2)
    subst, a=-3d/2c

    a^2 +ca+d=0
    (-3d/2c)^2 +c(-3d/2c)+d=0
    d=(2/9)(c^2)

    am I right?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,848
    Thanks
    321
    Awards
    1

    Re: quadratic equation

    Quote Originally Posted by Trefoil2727 View Post
    Given that the equation x^2 +cx+d=0 and x^2 +3cx+4d=0 have a common root, express d in term of c

    a+b=-c, a+q=-3c
    ab=d aq=4d
    aq-ab=3d
    a(q-b)=3d...(1)
    q-b=-2c...(2)
    subst, a=-3d/2c

    a^2 +ca+d=0
    (-3d/2c)^2 +c(-3d/2c)+d=0
    d=(2/9)(c^2)

    am I right?
    Put the value for d into your two quadratic equations and factor. They share a common solution x = -3c.

    -Dan
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor red_dog's Avatar
    Joined
    Jun 2007
    From
    Medgidia, Romania
    Posts
    1,252
    Thanks
    5

    Re: quadratic equation

    Substract de first ecuation from the second:
    2cx+3d=0
    The common root of the two quadratics is also the root of the last equation.
    So, the common root is x=-\frac{3d}{2c}
    Now replace x from any of the two quadratics with -\frac{3d}{2c}
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Quadratic Equation Help
    Posted in the Algebra Forum
    Replies: 2
    Last Post: December 29th 2010, 10:17 PM
  2. Replies: 3
    Last Post: April 25th 2010, 03:53 PM
  3. Quadratic Equation
    Posted in the Algebra Forum
    Replies: 1
    Last Post: March 18th 2010, 02:58 AM
  4. Quadratic Equation
    Posted in the Algebra Forum
    Replies: 2
    Last Post: October 14th 2009, 05:34 AM
  5. another quadratic equation
    Posted in the Algebra Forum
    Replies: 1
    Last Post: July 15th 2007, 11:05 AM

Search Tags


/mathhelpforum @mathhelpforum