Most Important Selected Qs for JEE AdvancedMathematicsTrigonometry
Consider the equation 1+ 3 2 x ^4 x+4 ^2 x + ^4 x+4 ^2 x = 2 ⁻¹( 2 x) x (- , )
Options
- ANumber of roots of this equation is 2
- BNumber of roots of this equation is 4
- COne root lies in the interval ( 8 , 6 )
- DIf x [0, n ] n N , number of roots will never be odd
Correct answer
D. If x [0, n ] n N , number of roots will never be odd
Step-by-step solution
aligned & ^4 x+4 ^2 x + ^4 x+4 ^2 x & = ^4 x-4 ^2 x+4 + ^4 x+4-4 ^2 x & =2- ^2 x+2- ^2 x=3 aligned equation reduces to = 1+ 2 x = 2 ⁻¹( 2 x) aligned & | x|= ⁻¹( 2 x) & f( / 8)=| / 8|- ⁻¹ / 4 aligned = / 8- / 4= 1+ 4 2 - / 4 0f( / 6)= | 6 |- ⁻¹ 3 = 3 2 - 3 0 so one root exists between ( / 8, / 6) .