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Question

If f(x)=x2+2bx+2c2 and g(x)=x22cx+b2 are such that min f(x) > max g (x), then relation between b and c, is


A

no relation

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B

0 < c <

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C

|c| <

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D

|c| < |b|

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Solution

The correct option is D

|c| < |b|


f(x)=(x+b)2+2c2b2min f(x)=2c2b2Also g(x)=x22cx+b2=b2+c2(x+c)2max g(x)=b2+c2

As min f(x) > max g (x), we get 2c2b2 > b2+c2

c2 > 2b2 |c| > 2|b|


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