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Without solving the equation, find the value of the roots

  1. Oct 14, 2013 #1
    1. The problem statement, all variables and given/known data

    23 - 5x - 4x2 = 0

    find ([itex]\alpha[/itex] - [itex]\beta[/itex])2



    2. Relevant equations

    In previous parts of the question i've calculated [itex]\alpha[/itex] + [itex]\beta[/itex], [itex]\alpha[/itex][itex]\beta[/itex], 1/[itex]\alpha[/itex] + 1/[itex]\beta[/itex] and ([itex]\alpha[/itex]+1)([itex]\beta[/itex]+1) but I can't think of any rules I know to help me solve the problem.

    3. The attempt at a solution

    Expanding ([itex]\alpha[/itex] - [itex]\beta[/itex])2

    gives

    [itex]\alpha[/itex]2+[itex]\beta[/itex]2 -2[itex]\alpha[/itex][itex]\beta[/itex]

    But I don't know what I can do with this info.

    I'd appreciate a nudge in the right direction!

    Thanks
     
  2. jcsd
  3. Oct 14, 2013 #2

    Office_Shredder

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    You can write your expression fairly simply in terms of [itex] \alpha+\beta [/itex] and [itex] \alpha \beta [/itex] (from which you can get the final answer according to your part 2)
     
  4. Oct 14, 2013 #3

    Mark44

    Staff: Mentor

    ##(\alpha - \beta)^2 = (\alpha + \beta)^2 - 4\alpha\beta##
    You said that you have already calculated ##\alpha + \beta ## and ##\alpha\beta ##.
     
  5. Oct 14, 2013 #4
    Gah, I should have seen that.

    Thanks!
     
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