Results 1 to 3 of 3

Math Help - polynomial of degree 3

  1. #1
    Newbie
    Joined
    Feb 2010
    Posts
    4

    polynomial of degree 3

    Hi,
    how would i find the roots for the following:

    x^3-4x+x+6=0

    thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Prove It's Avatar
    Joined
    Aug 2008
    Posts
    11,409
    Thanks
    1294
    Quote Originally Posted by dragonation View Post
    Hi,
    how would i find the roots for the following:

    x^3-4x+x+6=0

    thanks.
    I assume that this is actually

    x^3 - 4x^2 + x + 6 = 0.


    Using the remainder and factor theorems, we can see that when x= -1, the function = 0.

    So x + 1 is a factor.


    Using long division, we find that

    x^3 - 4x^2 + x + 6 = (x + 1)(x^2 - 5x + 6)

     = (x + 1)(x - 2)(x - 3).


    So now using the Null Factor Law:

    (x + 1)(x - 2)(x - 3) = 0

    x = -1 or x = 2 or x = 3.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor
    Joined
    Dec 2009
    Posts
    3,120
    Thanks
    1
    An unconventional way to view it is as follows,
    given that there are no more than 3 solutions,
    and works fine if the solutions are integers.

    x^3-4x^2+x+6=0

    x^3-4x^2=-x-6

    x^2(x-4)=-x-6

    x^2(4-x)=x+6

    x^2=\frac{x+6}{4-x}=g(x)

    You can examine x quite easily then...

    x=0,\ g(x)=\frac{6}{4}

    x=1,\ g(x)=\frac{7}{3}

    x=2,\ g(x)=\frac{8}{2}=4=2^2

    x=2 is a solution

    x=3,\ g(x)=\frac{9}{1}=3^2

    x=3 is a solution

    x=5,\ g(x)=\frac{10}{0}

    and higher values of x cannot yield a positive solution

    x=-1,\ g(x)=\frac{5}{5}=(-1)^2
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Polynomial of Degree 2
    Posted in the Differential Geometry Forum
    Replies: 5
    Last Post: January 19th 2011, 02:20 PM
  2. low degree polynomial
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: December 14th 2009, 01:40 AM
  3. 7th degree polynomial
    Posted in the Algebra Forum
    Replies: 1
    Last Post: January 24th 2009, 07:05 AM
  4. Polynomial of fifth degree
    Posted in the Calculus Forum
    Replies: 2
    Last Post: November 13th 2006, 07:25 AM
  5. 4th degree polynomial
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: September 27th 2005, 08:41 PM

Search Tags


/mathhelpforum @mathhelpforum