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Thread: Algeb

  1. #1
    Member srirahulan's Avatar
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    Post Algeb

    If the difference between the roots of $\displaystyle ax^2+bx+c=0 $ and $\displaystyle bx^2-cx+a=0 $ are equal.Prove $\displaystyle b^4 - a^2c^2 = 4ab(bc - a^2)$
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  2. #2
    Member Sylvia104's Avatar
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    Re: Algeb

    Hint: The roots of $\displaystyle px^2+qx+r=0$ $\displaystyle (p\ne0)$ are $\displaystyle \frac{-q\pm\sqrt{q^2-4pr}}{2p}$ so the difference between the roots is $\displaystyle \frac{\pm2\sqrt{q^2-4pr}}{2p} = \frac{\pm\sqrt{q^2-4pr}}p$
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