Question
Question: The number of solutions of the equation \(3\sin^{2}x - 7\sin x + 2 = 0\)in the interval \(\lbrack 0,...
The number of solutions of the equation 3sin2x−7sinx+2=0in the interval [0,5π] is
A
0
B
5
C
6
D
10
Answer
6
Explanation
Solution
3sin2x−7sinx+2=0⇒ 3sin2x−6sinx−sinx+2=0⇒(3sinx−1)(sinx−2)=0,
But sinx=2 so sinx=31. Hence from 0to2π=2 solution's (one in Ist quadrant and other in 2nd quadrant), from 2πto 4π=2 solution's and 4πto 5π=2 solution's. So total number of solutions=6.