QJEEM24Ma3ee9: JEE Main 2024 Mathematics - Class 11 JEEM24Ma3ee9 Solution: If 2 sin 3 ⁡ x + sin ⁡ 2 x cos ⁡ x + 4 sin ⁡ x − 4 = 0 has…

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QJEEM24Ma3ee9: JEE Main 2024 Mathematics - Class 11 JEEM24Ma3ee9 Solution: If 2 sin 3 ⁡ x + sin ⁡ 2 x cos ⁡ x + 4 sin ⁡ x − 4 = 0 has…

If $2 \sin^{3} x + \sin 2 x \cos x + 4 \sin x - 4 = 0$ has exactly 3 solutions in the interval $[0, \frac{n π}{2}], n \in N$ , then the roots of the equation $x^{2} + n x + (n - 3) = 0$ belong to :

Multiple Choice Options

A (0,∞)
B Z
C (−172,172)
D (−∞,0)

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$\begin{aligned} 2 \sin^{3} x + 2 \sin x \cdot \cos^{2} x + 4 \sin x - 4 = 0 \\ 2 \sin^{3} x + 2 \sin x \cdot (1 - \sin^{2} x) + 4 \sin x - 4 = 0 \\ 6 \sin x - 4 = 0 \\ \sin x = \frac{2}{3} \\ n = 5 (in the given interval) \\ x^{2} + 5 x + 2 = 0 \\ x = \frac{- 5 \pm \sqrt{17}}{2} \\ Required interval (- \infty, 0) \end{aligned}$

QJEEM24Ma3ee9: JEE Main 2024 Mathematics - Class 11 JEEM24Ma3ee9 Solution: If 2 sin 3 ⁡ x + sin ⁡ 2 x cos ⁡ x + 4 sin ⁡ x − 4 = 0 has…

Multiple Choice Options

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