Results 1 to 3 of 3

Math Help - Showing a root is of an equation

  1. #1
    Newbie
    Joined
    Oct 2009
    Posts
    16

    Showing a root is of an equation

    Show that 1 is a root of the equation x^3 - 13x + 12 = 0 I can usually do this by dividing the factor in to the equation but I can't seem to work this one out mainly because when I do it I end up having to take x^2 away from 13x which as far as I know you can't do. Any help on this one?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Amer's Avatar
    Joined
    May 2009
    From
    Jordan
    Posts
    1,093
    Quote Originally Posted by zyx.gar View Post
    Show that 1 is a root of the equation x^3 - 13x + 12 = 0 I can usually do this by dividing the factor in to the equation but I can't seem to work this one out mainly because when I do it I end up having to take x^2 away from 13x which as far as I know you can't do. Any help on this one?

    1 is he root of equation x^3-13x+12 if

    (1)^3 - 13(1) +12 = 0 and this is right

    and

    x^3-13x+12 = (x-1)(x^2+x-12)
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member pacman's Avatar
    Joined
    Jul 2009
    Posts
    448
    x^3 - 13x + 12 = 0,

    factor by grouping:

    x^3 +4x^2 - 4x^2 - 13x + 12 = 0,

    x^3 +4x^2 - 4x^2 - 13x - 3x + 3x + 12 = 0, group them

    (x^3 + 4x^2) + (- 4x^2 - 13x - 3x) + (3x + 12) = 0,

    (x^3 + 4x^2) + (- 4x^2 - 16x) + (3x + 12) = 0,

    x^2(x + 4) - 4x(x + 4) + 3(x + 4) = 0, factoring (x + 4),

    (x + 4)(x^2 - 4x + 3) = 0, now you left with a quadratic (x^2 - 4x + 3),

    this quadratic x^2 - 4x + 3 = 0 is easier to factor.

    . . . .
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Showing Analytic Using Derivative Equation
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: March 10th 2011, 10:10 AM
  2. Replies: 0
    Last Post: October 30th 2009, 01:36 PM
  3. showing differential equation solution
    Posted in the Differential Equations Forum
    Replies: 8
    Last Post: February 5th 2009, 10:20 PM
  4. Showing a parametric equation is smooth?
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: April 22nd 2008, 01:20 PM
  5. Replies: 1
    Last Post: March 29th 2008, 12:11 PM

Search Tags


/mathhelpforum @mathhelpforum