Suppose A, B, C are defined as A=a^2 b+a b^2-a^2 c-a c^2, B=b^2 c+b c^2-a^2 b-a b^2, and C=a^2 c+...

Suppose A, B, C are defined as A=a^2 b+a b^2-a^2 c-a c^2, B=b^2 c+b c^2-a^2 b-a b^2, and C=a^2 c+a c^2-b^2 c-b c^2,
where abc0 and the equation A x^2+B x+C=0 has equal roots, then a, b, c are in
(1) A.P.
(2) G.P.
(3) H.P.

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