The sum of three terms of a strictly increasing GP is $\alpha S$ and sum of their squares is $S^{2}$. $\alpha^{2}$ lies in

Question

$(a)\;(\frac{1}{3},2)\qquad(b)\;(\frac{1}{3},3)\qquad(c)\;(1,2)\qquad(d)\;None\;of\;these$