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Homework Help: Quadratic equation

  1. Sep 28, 2010 #1
    1. The problem statement, all variables and given/known data

    If one of the roots of the quadratic equation, ax^2+bx+c=0 is m+ni, show that the other root is m-ni.

    2. Relevant equations



    3. The attempt at a solution

    How do i actually show this? I mean it's a well known fact and a direct outcome of the quadratic formula. Is this valid?

    (x-(m+ni))(x-(m-ni))=0

    then x-2m+m^2+n^2=0
     
  2. jcsd
  3. Sep 28, 2010 #2

    Mark44

    Staff: Mentor

    The last equation above is not correct. For one thing, there should be an x2 term.

    You are given that m + ni is a root of the equation ax2 + bx + c = 0, so it should be true that a(m + ni)2 + b(m + ni) + c = 0.

    Expand the stuff on the left and you will get a complex number that must be zero.

    Now, what do you need to do to show that m - ni is also a solution of the same quadratic equation?
     
  4. Sep 28, 2010 #3
    thanks Mark!
     
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