JEE Mains · Maths · STD 11 - 4.2 Quadratic equations and inequations
Let \(S=\left\{\sin ^2 2 \theta:\left(\sin ^4 \theta+\cos ^4 \theta\right) x^2+(\sin 2 \theta) x+\right.\) \(\left(\sin ^6 \theta+\cos ^6 \theta\right)=0\) has real roots\(\}\). If \(\alpha\) and \(\beta\) be the smallest and largest elements of the set \(S\), respectively, then \(3\left((\alpha-2)^2+(\beta-1)^2\right)\) equals ...........
- A \(4\)
- B \(2\)
- C \(7\)
- D \(9\)
Answer & Solution
Correct Answer
(A) \(4\)
Step-by-step Solution
Detailed explanation
\( \mathrm{D}=(\sin 2 \theta)^2-4\left(1-\frac{\sin ^2 2 \theta}{2}\right)\left(1-\frac{3}{4} \sin ^2 2 \theta\right) \) \( =(\sin 2 \theta)^2-4\left(1-\frac{5}{4} \sin ^2 2 \theta+\frac{3}{8} \sin ^4 2 \theta\right) \)…
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