If non - zero real numbers b and c are such that min f(x) > max g(x) , where $\;f(x)=x^{2}+2bx+2c^{2}\;$ and $\;g(x)=-x^{2}-2cx+b^{2}\;(x \in R)\;$ ;then $\;|\large\frac{c}{b}|\;$ lies in the interval :

Question

$(a)\;(0,\large\frac{1}{2})\qquad(b)\;[\large\frac{1}{2},\large\frac{1}{\sqrt{2}})\qquad(c)\;[\large\frac{1}{\sqrt{2}},\normalsize \sqrt{2}]\qquad(d)\;(\sqrt{2} , \infty)$