If $f(x) = x^2 + 2bx + 2c^2$ and $g(x) =

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Relations and Functions

Question:

If $f(x) = x^2 + 2bx + 2c^2$ and $g(x) = −x^2 − 2cx + b^2$ are such that min f(x) > max g(x), then the relation between b and c, must be

Options:

no relation

$0<c<\frac{b}{2}$

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

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

Correct Answer:

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

Explanation:

$f(x) = x^2 + 2bx + 2c^2⇒\min f(x)=2c^2-b^2$

$g(x) = −x^2 − 2cx + b^2⇒\max g(x)=c^2+b^2$

Now, min f(x) > max g(x)m $⇒ 2c^2-b^2>c^2+b^2⇒c^2>2b^2⇒|c|>|b|\sqrt{2}$