Results 1 to 3 of 3

Thread: [SOLVED] Proving?

  1. #1
    Member
    Joined
    May 2009
    Posts
    99

    [SOLVED] Proving?

    If $\displaystyle (x - a)^2$ is a factor of $\displaystyle x^3 + mx^2 + n$, prove that $\displaystyle 27n + 4m^3 = 0$
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor red_dog's Avatar
    Joined
    Jun 2007
    From
    Medgidia, Romania
    Posts
    1,252
    Thanks
    5
    Let $\displaystyle f(x)=x^3+mx^2+n$

    If $\displaystyle (x-a)^2$ is a factor of f, then $\displaystyle f(a)=0, \ f'(a)=0$

    $\displaystyle f(a)=0\Rightarrow a^3+ma^2+n=0$

    $\displaystyle f'(a)=0\Rightarrow 3a^2+2am=0\Rightarrow a(3a+2m)=0$

    If $\displaystyle a\neq 0\Rightarrow a=-\frac{2m}{3}$

    Now replace a in $\displaystyle f(a)=0$
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Member
    Joined
    May 2009
    Posts
    99
    Lol Thanks. I nearly found it but my a was $\displaystyle \frac{-2}{3}$. Thanks for clearing it up for me.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Proving subgroups
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: Dec 9th 2009, 06:49 AM
  2. [SOLVED] Proving equality - help please..
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: Dec 7th 2009, 05:18 AM
  3. [SOLVED] proving limits
    Posted in the Calculus Forum
    Replies: 2
    Last Post: Oct 4th 2009, 12:46 PM
  4. [SOLVED] Proving problem
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: Aug 17th 2009, 12:02 AM
  5. [SOLVED] Proving
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: Jul 30th 2009, 08:27 AM

Search Tags


/mathhelpforum @mathhelpforum