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JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
Let \(S\) be the set of all \(\alpha \in R\) such that the equation, \(cos\,2 x + \alpha \,sin\, x = 2\alpha -7\) has a solution. Then \(S\) is equal to
- A \([3, 7]\)
- B \(R\)
- C \([2, 6]\)
- D \([1, 4]\)
Answer & Solution
Correct Answer
(C) \([2, 6]\)
Step-by-step Solution
Detailed explanation
Given, \(\cos 2 x+2 \sin x=2 \alpha-7\) \(\Rightarrow 1-2 \sin ^{2} x+\alpha \sin x=2 \alpha-7\) \(\Rightarrow 2 \sin ^{2} x-\alpha \sin x+2 \alpha-8=0\) \(\Rightarrow \sin x=\frac{\alpha \pm \sqrt{\alpha^{2}-8(2 \alpha-8)}}{4}\)…
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