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Math Help - [SOLVED] Prove the existence of quadratic roots

  1. #1
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    [SOLVED] Prove the existence of quadratic roots

    If ab>0 and bc<0, then ax^2+bx+c=0 has two real solutions. (Prove this)

    I started, but I don't know.

    Let a, b, c be real.
    Assume ab>0 and bc<0.
    So bc<ab
    So c>a.
    So....

    I don't know from here. It clearly involves showing that the discriminant, b^2-4ac is positive I would think. How I can go about doing so, not sure.

    Thanks for the help.
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  2. #2
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    ab > 0 and bc < 0

    case 1 ...

    a and b both > 0 ... then c < 0

    then ac < 0, -4ac > 0

    b^2 - 4ac > 0 ... two distinct real roots

    case 2 ...

    a and b both < 0 ... then c > 0

    ac < 0 , -4ac > 0

    b^2 - 4ac > 0 ... two distinct real roots
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