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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- May 16th 2012, 05:57 AMsrirahulanAlgeb
If the difference between the roots of $\displaystyle ax^2+bx+c=0 $ and $\displaystyle bx^2-cx+a=0 $ are equal.Prove $\displaystyle b^4 - a^2c^2 = 4ab(bc - a^2)$

- May 16th 2012, 06:12 AMSylvia104Re: 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 $\displaystyle \frac{\pm2\sqrt{q^2-4pr}}{2p} = \frac{\pm\sqrt{q^2-4pr}}p$