Let A. G^2 and H be the roots ofcubic e...

Let `A. G^2 and H` be the roots ofcubic equation `x^3+px^2 + qx + r=0` which are in GP, where p, q are integers and `A,G,H` are respeetiveI `AM, GM, HM` of two positive numbers. If `p, q in (-100, 100)`,then number ofall possible ordered triplets `(p, q, r)` is

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