# Algeb

If the difference between the roots of $ax^2+bx+c=0$ and $bx^2-cx+a=0$ are equal.Prove $b^4 - a^2c^2 = 4ab(bc - a^2)$
Hint: The roots of $px^2+qx+r=0$ $(p\ne0)$ are $\frac{-q\pm\sqrt{q^2-4pr}}{2p}$ so the difference between the roots is $\frac{\pm2\sqrt{q^2-4pr}}{2p} = \frac{\pm\sqrt{q^2-4pr}}p$