JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
Let \(S=\left\{\alpha: \log _2\left(9^{2 \alpha-4}+13\right)-\log _2\left(\frac{5}{2} \cdot 3^{2 \alpha-4}+1\right)=2\right\} .\) Then the maximum value of \(\beta\) for which the equation \(x^2-2\left(\sum_{a \in} \alpha\right)^2 x+\sum_{a \in}(\alpha+1)^2 \beta=0\) has real roots, is \(...........\)
- A \(24\)
- B \(25\)
- C \(23\)
- D \(22\)
Answer & Solution
Correct Answer
(B) \(25\)
Step-by-step Solution
Detailed explanation
\(\log _2\left(9^{2 \alpha-4}+13\right)-\log _2\left(\frac{5}{2} \cdot 3^{2 \alpha-4}+1\right)=2\) \(\Rightarrow \frac{9^{2 \alpha-4}+13}{\frac{5}{2} 3^{2 \alpha-4}+1}=4\) \(\Rightarrow \alpha=2 \quad \text { or }\)…
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