Results 1 to 4 of 4

Math Help - Quadratic and cubic equation -show that -(common roots)

  1. #1
    Junior Member
    Joined
    Aug 2011
    Posts
    43

    Quadratic and cubic equation -show that -(common roots)

    If the equations ax^2+bx+c=0 and x^3+3x^2+3x+2=0 have two common solutions then show a=b=c.


    first equation will be the factor of second.
    taking out common from first equation.


    how to show a=b=c??
    please provide hints.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4

    Re: Quadratic and cubic equation -show that -(common roots)

    Quote Originally Posted by sumedh View Post
    If the equations ax^2+bx+c=0 and x^3+3x^2+3x+2=0 have two common solutions then show a=b=c.


    first equation will be the factor of second.
    taking out common from first equation.


    how to show a=b=c??
    please provide hints.
    This means that ax^2+bx+c is a factor of ax^3+3ax^2+3ax+2a. Perform polynomial long division and set the remainder to zero.

    (this process give the required solution and one other solution, but the second solution when checked is a spurious solution)

    CB
    Last edited by CaptainBlack; August 19th 2011 at 10:55 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Aug 2011
    Posts
    43

    Re: Quadratic and cubic equation -show that -(common roots)

    can we solve by the following formulas

    for quadratic eqs.
    α+ =-b/a

    α= c/a

    for cubic equations
    (Γ=gamma)

    α++Γ=-b/a

    (α)+(Γ)+(αΓ)=c/a

    αΓ=-d/a



    i am trying to solve by this method but i hung up! in between?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Aug 2011
    Posts
    43

    Re: Quadratic and cubic equation -show that -(common roots)

    thank you very much i got it
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Roots of cubic equations and new equation
    Posted in the Algebra Forum
    Replies: 1
    Last Post: January 13th 2010, 03:46 AM
  2. Roots of cubic equations and new equation
    Posted in the Algebra Forum
    Replies: 11
    Last Post: January 4th 2010, 02:49 PM
  3. Roots of a cubic equation
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: January 3rd 2010, 01:59 PM
  4. Roots of cubic equation
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: October 11th 2009, 06:35 AM
  5. Replies: 4
    Last Post: October 16th 2008, 04:46 AM

/mathhelpforum @mathhelpforum