TS EAMCET · Maths · Quadratic Equation
If the maximum value of \(2 x-7-a x^2\) cannot exceed 20 , then the minimum value of \(a\) is
- A 27
- B \(\frac{1}{13}\)
- C 13
- D \(\frac{1}{27}\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{27}\)
Step-by-step Solution
Detailed explanation
We have, \[ \begin{aligned} & f(x)=2 x-7-a x^2 \\ & f(x)=-7-a\left(x^2-\frac{2}{a} x\right) \\ & f(x)=\frac{1}{a}-7-a\left(x^2-\frac{2 x}{a}+\frac{1}{a^2}\right) \\ & f(x)=\frac{1}{a}-7-a\left(x-\frac{1}{a}\right)^2 \end{aligned} \] Maximum value of \(f(x)\) is \(\frac{1}{a}-7\)…
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