The number of values of x in the interval [0 , 5 π ] satisfying the equation 3sin2 x-7sin ⁡ x+2=0 is

Question

The number of values of x in the interval [0 , 5 π ] satisfying the equation 3sin2 x-7sin ⁡ x+2=0 is (A) 0 (B) 5 (C) 6 (D) 10

Tardigrade Admin · Accepted Answer

3sin2 x-7sin â¡ x+2=0 3sin2 x-6sin â¡ x-sin â¡ x+2=0 (3 sin x - 1)(sin â¡ x - 2)=0 ⇒ sin x=(1/3),sin â¡ x=2 not possible <img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/m-rdewzib0dksi.png" /> Fro the figure, 6 roots in [0 , 5 π ]

Q. The number of values of $x$ in the interval $[0, 5 π]$ satisfying the equation $3 s i n^{2} x - 7 s in x + 2 = 0$ is

$0$

$5$

$6$

$10$

$3 s i n^{2} x - 7 s in x + 2 = 0$
$3 s i n^{2} x - 6 s in x - s in x + 2 = 0$
$(3 s in x - 1) (s in x - 2) = 0$
$\Rightarrow s in x = \frac{1}{3}, s in x = 2$ not possible

Fro the figure, $6$ roots in $[0, 5 π]$

Q. The number of values of x in the interval [0,5π] satisfying the equation 3sin2x−7sin⁡x+2=0 is

0

5

6

10

3sin2x−7sin⁡x+2=0 3sin2x−6sin⁡x−sin⁡x+2=0 (3sinx−1)(sin⁡x−2)=0 ⇒sinx=31​,sin⁡x=2 not possible Fro the figure, 6 roots in [0,5π]

Q. The number of values of $x$ in the interval $[0, 5 π]$ satisfying the equation $3 s i n^{2} x - 7 s in x + 2 = 0$ is

$0$

$5$

$6$

$10$

$3 s i n^{2} x - 7 s in x + 2 = 0$
$3 s i n^{2} x - 6 s in x - s in x + 2 = 0$
$(3 s in x - 1) (s in x - 2) = 0$
$\Rightarrow s in x = \frac{1}{3}, s in x = 2$ not possible

Fro the figure, $6$ roots in $[0, 5 π]$