Results 1 to 4 of 4

Math Help - Quadratics question

  1. #1
    Senior Member
    Joined
    Oct 2009
    Posts
    459

    Quadratics question

    I don't know how to do this question:

    Given that alpha is a root of the equation x^2=2x-3 show that alpha^3=alpha-6.

    I have a list of equations involving the roots calling them alpha and beta.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Thanks
    1
    Hello Stuck Man
    Quote Originally Posted by Stuck Man View Post
    I don't know how to do this question:

    Given that alpha is a root of the equation x^2=2x-3 show that alpha^3=alpha-6.

    I have a list of equations involving the roots calling them alpha and beta.
    If \alpha is a root, then:
    \alpha^2=2\alpha-3 (1)
    Multiply both sides by \alpha:
    \Rightarrow \alpha^3 = (2\alpha-3)\alpha
    =2\alpha^2-3\alpha

    = 2(2\alpha -3)-3\alpha, using (1)
    I'm sure you can complete it now.

    Grandad
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Oct 2009
    Posts
    459
    I see, thanks.

    Is there any particular topic that results such as this are in?:
    a^2+b^2=(a+b)^2-2ab
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570
    Thanks
    1
    Hello Stuck Man
    Quote Originally Posted by Stuck Man View Post
    I see, thanks.

    Is there any particular topic that results such as this are in?:
    a^2+b^2=(a+b)^2-2ab
    Not really. It's part of general algebraic manipulation, which will turn up in all sorts of situations - in particular, the solution of polynomial equations, factorisation, etc.

    Grandad
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Quadratics question
    Posted in the Algebra Forum
    Replies: 4
    Last Post: June 6th 2009, 10:22 PM
  2. Quadratics question... AGAIN!!! :D
    Posted in the Algebra Forum
    Replies: 6
    Last Post: July 8th 2008, 01:23 PM
  3. Quadratics Question
    Posted in the Algebra Forum
    Replies: 9
    Last Post: July 7th 2008, 02:27 PM
  4. Quadratics Question
    Posted in the Math Topics Forum
    Replies: 5
    Last Post: November 11th 2007, 12:45 PM
  5. one last quadratics question!
    Posted in the Algebra Forum
    Replies: 2
    Last Post: April 22nd 2007, 09:02 PM

Search Tags


/mathhelpforum @mathhelpforum