AP EAMCET · Maths · Quadratic Equation
For real number \(x\), if the minimum value of \(f(x)=x^2+2 b x+2 c^2\) is greater than the maximum value of \(g(x)=-x^2-2 c x+b^2\), then
- A \(c^2>2 b^2\)
- B \(c^2 < 2 b^2\)
- C \(b^2=2 c^2\)
- D \(c^2=2 b^2\)
Answer & Solution
Correct Answer
(A) \(c^2>2 b^2\)
Step-by-step Solution
Detailed explanation
We have, \[ \begin{aligned} f(x) & =x^2+2 b x+2 x^2 \\ & =(x+b)^2+2 x^2-b^2 \end{aligned} \] \(\therefore\) Minimum value of…
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