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Math Help - Quadratic equation

  1. #1
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    Quadratic equation

    If the Quadratic equation αx2 + βx + a2 + b2 + c2 – ab – bc – ca = 0 has imaginary roots, then

    Prove that

    2(α – β ) + (a-b)2 + (b-c)2 + (c-a)2 < 0
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  2. #2
    Senior Member DivideBy0's Avatar
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    Just to clear things up, do you mean:

    ax^2+\beta x+a^2+b^2+c^2-ab-bc-ac=0

    Prove that:

    2(a-\beta)+(a-b)^2+(b-c)^2+(c-a)^2<0?

    Next time you want to show powers use the '^' symbol. e.g 2^n is 2^n.
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by nsprasad2001 View Post
    If the Quadratic equation αx2 + βx + a2 + b2 + c2 – ab – bc – ca = 0 has imaginary roots, then

    Prove that

    2(α – β ) + (a-b)2 + (b-c)2 + (c-a)2 < 0
    The descriminant has to be negative.

    RonL
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  4. #4
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    Quadratic equation

    Yes
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