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If $f (x) = x^{2} + 2 b x + 2 c^{2} a n d g (x) = - x^{2} - 2 c x + b^{2}$ are such that min f(x) > max g(x), then the relation between b and c is

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detailed solution

Correct option is D

f(x)=x2+2bx+2c2=(x+b)2+2c2−b2⇒ minf(x)=2c2−b2 Also g(x)=−x2−2cx+b2 =b2+c2−(x+c)2 So maxg(x)=b2+c2 Since minf(x)>maxg(x) So 2c2−b2>b2+c2⇒ c2>2b2⇒|c|>2|b|

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

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Ready to Test Your Skills?

free study material

If $f (x) = x^{2} + 2 b x + 2 c^{2} a n d g (x) = - x^{2} - 2 c x + b^{2}$ are such that min f(x) > max g(x), then the relation between b and c is