question_answer

If \[(x)={{x}^{2}}+2bx+2{{c}^{2}}\]and \[g(x)=-{{x}^{2}}-2cx+{{b}^{2}}\] such that min. f (x) > max. g(x), then the relation between b and c, is:

A)  No real value of b and c

B)  \[0<c<b\sqrt{2}\]

C)  \[|c|\,<\,|b|\sqrt{2}\]

D)  \[|c|\,>\,|b|\sqrt{2}\]

E)  None of these