If f ( x ) = x 2 + 2 b x + 2 c 2 and g ( x ) = − x 2 − 2 c x + b 2 are such that min f ( x ) max g ( x ) , then relation between b and c , is

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

TestHub · Accepted Answer

f ( x ) = ( x + b ) 2 + 2 c 2 − b 2 ⇒ min f ( x ) = 2 c 2 − b 2 Also g ( x ) = − x 2 − 2 c x + b 2 = b 2 + c 2 − ( x + c ) 2 ⇒ max g ( x ) = b 2 + c 2 As min f ( x ) > max g ( x ) , we get 2 c 2 − b 2 > b 2 + c 2 ⇒ c 2 > 2 b 2 ⇒ ∣ c ∣ > 2 ​ ∣ b ∣

Mathematics - Quadratic Equation Question with Solution | TestHub

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