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Math Help - |alpha-beta|

  1. #1
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    |alpha-beta|

    Supposing ax^2 + bx +c = 0 (this isn't actually the equation, but I'll have a better chance of understanding in general form):

    I've been told to find the value of the usual root stuff ( \alpha + \beta ( -b/a), \alpha\beta ( c/a), \alpha^2 + \beta^2). All good; but then it says "without finding the values of \alpha or \beta, find | \alpha - \beta|.

    I'm wondering how to rearrange that to use only \alpha + \betas and \alpha\betas.

    Any help would be greatly appreciated.
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  2. #2
    MHF Contributor red_dog's Avatar
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    |\alpha-\beta|=\sqrt{(\alpha-\beta)^2}=\sqrt{\alpha^2+\beta^2-2\alpha\beta}=\sqrt{(\alpha+\beta)^2-4\alpha\beta}
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