If $x^2-ax+b=0$ and $x^2-cx+d=0$ have a common root, then show that $ab,bc,ad $ are in an arithmetic progression
When I use the relationship for the common root for qudratic equations, i end up with $(c-a)(ad-bc)=(b-d)^2$. By solving this i cannot obtain $2bc=ab+ad$. Is there any more thing to concern? Or the question is wrong(some data missing)?