if ax2+2bx+c=0 and a1x2+2b1x+c1 have a common root and

a/a1 ,b/b1 ,c/c1 are in A.P.

show that a1,b1,c1 are in G.P.

I know the mean formula of A.P. i.e. the middle term is the mean of the other two.

any hints of which formula of G.P. to use and how to solve???