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MCQMediumJEE Main 2024 · 30 January, Shift 1Trigonometric Equations

Mathematics Question from JEE Main 2024 · 30 January, Shift 1

If 2sin⁡3x+sin⁡2xcos⁡x+4sin⁡x−4=02\sin^3 x + \sin 2x \cos x + 4\sin x - 4 = 0 has exactly 33 solutions in the interval [0,nπ2]\left[0, \frac{n\pi}{2}\right], n∈Nn \in \mathbb{N}, then the roots of the equation x2+nx+(n−3)=0x^2 + nx + (n-3) = 0 belong to:

  • A

    (0,∞)(0, \infty)

  • B

    (−∞,0)(-\infty, 0)

  • C

    (−172,172)\left(-\frac{\sqrt{17}}{2}, \frac{\sqrt{17}}{2}\right)

  • D

    Z\mathbb{Z}

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