Results 1 to 2 of 2

Math Help - Factor Theroem

  1. #1
    Newbie
    Joined
    Apr 2012
    From
    United Kingdom
    Posts
    6

    Factor Theroem

    Use the Factor Theorem to find the real number k such that (z k) is a factor of z^3 + (-6 + 2j) z ^2 + (12 - 15j) z + (-9+27j)
    Hence write z^3 + (-6 + 2j) z ^2 + (12 - 15j) z + (-9+27j) as the product of two factors.

    Find all the solutions of the equation z^3 + (-6 + 2j) z ^2 + (12 - 15j) z + (-9+27j).
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Apr 2005
    Posts
    15,372
    Thanks
    1314

    Re: Factor Theroem

    Then "factor theorem" says that any polynomial of the form z^3+ az^2+ bz+ c can be factored as (z- z_0)(z- z_1)(z- z_2) where z_0, z_1, z_2 are complex numbers and, of course, they make the value of the polynomial 0. One of the things that tells us is that the product of those numbers is c= -9+ 27j= -9(1+ 3j). Crossing my fingers and trying (something I strongly recommend!) I see that if I set z= 3, I get 27+ (-6+2j)(9)+ (12- 15j)(3)+ (-9+ 27j)= (27- 54+ 36- 9)+ j(2(9)- 15(3)+ 27)= (63- 63)+ j(18- 45+ 27)= 0!

    Can you finish the problem now?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. The Squeeze Theroem
    Posted in the Calculus Forum
    Replies: 3
    Last Post: September 9th 2010, 04:59 AM
  2. Darboux Theroem
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: February 1st 2010, 06:32 AM
  3. comparison theroem
    Posted in the Calculus Forum
    Replies: 3
    Last Post: November 1st 2009, 12:32 PM
  4. Mean Value Theroem
    Posted in the Calculus Forum
    Replies: 3
    Last Post: October 10th 2009, 11:48 PM
  5. Factor Theroem
    Posted in the Algebra Forum
    Replies: 2
    Last Post: February 13th 2007, 07:37 PM

Search Tags


/mathhelpforum @mathhelpforum