
Quadratics #1
If the roots of (ca)x^2 + (ab)x + (bc) = 0 are equal, show that a,c,b are in arithmetic progression.
What I did was:
For the roots to be equal, the disciminant must be equal to zero.
Thus, discriminant = (ab)^2  4(ca)(bc) = 0
Eventually, I got a^2 + 6ab + b^2 + 4c^2  4bc  4ac = 0 but I don't know how to use this to solve the problem.
Please, any help?

You made a mistake. The discriminant is
$\displaystyle a^2+b^2+4c^2+2ab4bc4ac=(a+b2c)^2$
The discriminant must be 0, so $\displaystyle a+b2c=0\Rightarrow c=\frac{a+b}{2}$, then a, c, b are in arithmetic progression.