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If non-zer real numbers b and c are such that min `f(x) gt max (g)x,` where `f(x)=x^(2)+2bx+2c^(2) and g(x)=-x^(2)-2cx+b^(2)(x in R)`, Then `|(c)/(b)|` lies in the interval

A

`(0,(1)/(2))`

B

`[(1)/(2),(1)/(sqrt(2)))`

C

`[(1)/(sqrt(2)),sqrt(2)]`

D

`(sqrt(2),oo)`

Text Solution

Verified by Experts

The correct Answer is:
D
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