Results 1 to 5 of 5

Math Help - Find the roots of the cubic equation

  1. #1
    Junior Member
    Joined
    Apr 2012
    From
    bowie md
    Posts
    34

    Find the roots of the cubic equation

    What are the roots of the cubic equcation x3-8x-3=0?

    Ans: D. x=-2.62, -0.38, 3

    1. step
    x3-8x-3 = x2+3x-1 By inspection +3 is a root, and x-3 is a factor. Factor out (x-3)
    x-3

    Please do whole the problem. How did they get x2+3x-1=0
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member Goku's Avatar
    Joined
    Mar 2011
    From
    South Africa
    Posts
    84
    Thanks
    10

    Re: Find the roots of the cubic equation

    It supposed to be x^2+3x+1, the division is incorrect...
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Mar 2012
    From
    Sheffield England
    Posts
    440
    Thanks
    76

    Re: Find the roots of the cubic equation

    We know that (x-3)( )=x^3-8x+3 We want to find the empty bracket. It must start with x^2 and end in -1
    So (x-3)(x^2 -1)=X^3-8x+3. We notice that there is no x^2 term in the answer. With the brackets as we have them so far we would have -3x^2 in the answer. So we still need +3x^2. This we will have if we add +3x to the second bracket.
    If you know how to do long division you could get this from (x^3-8x-3) divided by (x-3)
    So x-3=0 or x^2+3x+1= 0 which you solve using the quadratic equation formula.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member
    Joined
    Nov 2011
    From
    Crna Gora
    Posts
    420
    Thanks
    64

    Re: Find the roots of the cubic equation

    x^3-8x-3=x^3-8x-27+24=(x^3-3^3)-8(x-3)=

    =(x-3)(x^2+3x+9)-8(x-3)=(x-3)(x^2+3x+1)

    Hence :

    x_1=3

    x_{2,3}=\frac{-3 \pm \sqrt 5}{2}
    Last edited by princeps; April 12th 2012 at 01:19 AM.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Apr 2012
    From
    bowie md
    Posts
    34

    Re: Find the roots of the cubic equation

    Is long division ideal to use on ployimonal that has a missing x^2 or is skips a power such it goes from x^3 to x and misses the x^2
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Complex Roots to Cubic Equation
    Posted in the Algebra Forum
    Replies: 3
    Last Post: April 9th 2012, 10:14 AM
  2. Forming a Cubic Equation from Roots
    Posted in the Pre-Calculus Forum
    Replies: 6
    Last Post: September 13th 2010, 04:31 PM
  3. Roots of cubic equations and new equation
    Posted in the Algebra Forum
    Replies: 1
    Last Post: January 13th 2010, 03:46 AM
  4. Roots of a cubic equation
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: January 3rd 2010, 01:59 PM
  5. Roots of cubic equation
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: October 11th 2009, 06:35 AM

Search Tags


/mathhelpforum @mathhelpforum