99 Percentile Qs Bank for JEE MainMathematicsTrigonometric Equations
The general solution of the equation 3-5 x+ ^2 x + x=0 is
Options
- An +(-1)^n 6 , n Z
- B2 n 6 , n Z
- C(2 n+1) - 6 , n Z
- D2 n 5 6 , n Z
Correct answer
C. (2 n+1) - 6 , n Z
Step-by-step solution
Given equation, gathered 3-5 x+ ^2 x + x=0 3-5 x+ ^2 x =- x, x gathered On squaring both sides, we get array lrl & 3-5 x+ ^2 x= ^2 x & 2 ^2 x-5 x+2=0 & 2 ^2 x-4 x- x+2=0 & 2 x( x-2)-1( x-2)=0 & x= 1 2 or 2 & x [-1,1] & x= 1 2 and x < 0 array Means, x= 1 2 and x= - 3 2 Therefore, x=(2 n+1) - 6 , n Z .