1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

X^3 - 4x^2 + 4x +2 = 0

  1. Nov 23, 2012 #1
    1. The problem statement, all variables and given/known data
    Please see the method of solving the equation x^3 -4x^2 + 4x +2 = 0 from the attached.
    In the red brackets,can anyone explain why the negative root is not involved in the calculation?
    by the quadratic formula,
    z = [y±√(y^2 - 4k)]/2
    so why only y+√(y^2 - 4k) is considered?
    and in the second bracket,again,why the another root of u ,(-1/27)(-35 - 3√129),is not used?
    Both roots are negative.
    Thx.
    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

    • a.jpg
      a.jpg
      File size:
      50.3 KB
      Views:
      117
    • b.jpg
      b.jpg
      File size:
      22.9 KB
      Views:
      108
  2. jcsd
  3. Nov 23, 2012 #2

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    hi davon806! :wink:
    you can use the "negative" root in either or both cases, and it should give the same result in the end …

    have you tried it? :smile:
     
  4. Nov 24, 2012 #3
    As there are 2 solutions of z and 2 solutions of u,
    there are 4 possible answers for x
    z = [y ± √(y^2 - 4k)]/2 , u = 1/27(-35 ± 3√129)
    if both of the signs are +,or both signs are -,the value of x would be:
    x = 4/3 - 4/[3(35-3√129)^(1/3) - 1/3(35-3√129)^(1/3)]
    if z = [y+√(y^2 - 4k)]/2 and u = (-35-3√129)/27 ,
    x = 4/3 - 4/[3(35+3√129)^(1/3) - 1/3(35+3√129)^(1/3)]

    What's wrong?Thx.
     
  5. Nov 24, 2012 #4

    tiny-tim

    User Avatar
    Science Advisor
    Homework Helper

    hi davon806! :smile:
    ah, but 1/(35-3√129) = (35+3√129)/64 :wink:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook