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Trigonometric Functions and Equations question

2024 · 30 Jan · Shift 1 · Q47

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JEE Main
Mathematics
Trigonometric Functions and Equations
2024 · 30 Jan · Shift 1 · Q47

Trigonometric Functions and Equations question

2024 · 30 Jan · Shift 1 · Q47

JEE MainMathematicsTrigonometric Functions and EquationsMCQ+4 / −1

If

2 \sin ^3 x+\sin 2 x \cos x+4 \sin x-4=0

has exactly 3 solutions in the interval

\left[0, \frac{\mathrm{n} \pi}{2}\right], \mathrm{n} \in \mathrm{N}

, then the roots of the equation

x^2+\mathrm{n} x+(\mathrm{n}-3)=0

belong to :

A
$(0, \infty)$
B
Z
C
$\left(-\frac{\sqrt{17}}{2}, \frac{\sqrt{17}}{2}\right)$
D
$(-\infty, 0)$

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