Question

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

• A. Non real values of b and c
• B. 0 < c <$\sqrt{2}b$
• C. |c| <$\sqrt{2}$ |b|
• D. |c| >$\sqrt{2}$| b |

Answer 1

Answer: (D)

|c| >$\sqrt{2}$| b |

Answer 2

min f(x) > max g(x)

⇒ $\frac{8c^{2} - 4b^{2}}{4} > \frac{4c^{2} + 4b^{2}}{4}$

⇒ 2c² – b² > b² + c² ⇒ c² – 2b² > 0

⇒ |c| >$\sqrt{2}$ |b|