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Quadratic discriminant with tricky algebra

  1. Jul 18, 2016 #1
    1. The problem statement, all variables and given/known data
    Capture.png

    2. Relevant equations
    Quadratic discriminant

    3. The attempt at a solution
    I did b^2 -4ac>=0, but the algebra becomes prohibitively difficult.
     
  2. jcsd
  3. Jul 18, 2016 #2

    Ray Vickson

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    Sometimes there are just no shortcuts, and lengthy algebra cannot be avoided. That being said, I am not sure the result sought is correct; in particular, in your second equation you have a constant ##d## appearing in it, but there is no ##d## in the first equation.
     
  4. Jul 18, 2016 #3
    I got something like
    ab-4ac-ad+bc+bd-cd but I can't seem to work around that.
     
  5. Jul 18, 2016 #4
    In the second equation there is a misprint
    The correct equation is
    (a+c-b)x2-2(a-c)x+(a+c+b) = 0
    The proof is not difficult. Just find the discriminant.
     
  6. Jul 18, 2016 #5

    Ray Vickson

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    What about the issue I raised? There is a ##d## in the second equation, but no ##d## in the first one. The relation between ##a,b,c## arising from the first equation does not involve any ##d## at all.
     
  7. Jul 18, 2016 #6
    Thanks - I guess there's a misprint in my book after all.
     
  8. Jul 18, 2016 #7
    Strangely enough I got -b^2 -4ac, which isn't right.

    Update - I found an algebraic slip in my working.
     
  9. Jul 18, 2016 #8
    I have managed to work the first part - but I don't have a clue on tackle the second part.

    Update - I managed to work this out.
     
    Last edited: Jul 18, 2016
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