Let $$a,\,b,\,c$$ be positive integers in arithmetic progression such that the equation

$$ax^2+bx+c=0$$

has only integer solutions.

Then which of the following statements is (are) TRUE?

A

$$c-b$$ is an integer multiple of $$a$$

B

Both the roots of the equation $$ax^2+bx+c=0$$ are odd integers

C

If $$c=15$$, then $$ab=8$$

D

If $$b=8$$, then $$x=3$$ is a root of the equation $$ax^2+bx+c=0$$