Home
Class 12
MATHS
If the equation x^(2)+12+3sin(a+bx)+6x=0...

If the equation `x^(2)+12+3sin(a+bx)+6x=0` has atleast one real solution, where `a, b in [0,2pi]`, then the value of a - 3b is `(n in Z)`

A

`2n pi`

B

`(2n+1)pi`

C

`(4n-1)(pi)/(2)`

D

`(4n+1)(pi)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
`x^(2)+12+3 sin (a+bx)+6x =0`
`rArr (x+3)^(2)+3+3sin (a+bx)=0`
`rArr (x+3)^(2)+3=-3 sin (a+ bx)`
`L.H.S. ge 3` but `R.H.S. le 3`
`L.H.S. = R.H.S. = 3`
`therefore x=-3` and `sin (a + bx) =-1`
`rArr sin (a-3b)=-1`
or `a-3b=(4n-1)(pi)/(2), n in Z`
Promotional Banner

Similar Questions

Explore conceptually related problems

If the equation x^(2)+4+3sin(ax+b)-2x=0 has at least one real solution, where a,b in [0,2pi] then one possible value of (a+b) can be equal to

If the equation sin ^(2) x - k sin x - 3 = 0 has exactly two distinct real roots in [0, pi] , then find the values of k .

If a , b in [0,2pi] and the equation x^2+4+3sin(a x+b)-2x=0 has at least one solution, then the value of (a+b) can be (7pi)/2 (b) (5pi)/2 (c) (9pi)/2 (d) none of these

If the equation ax^(2) + bx + 6 = 0 has real roots, where a in R, b in R , then the greatest value of 3a + b, is

If a , b in [0,2pi] and the equation x^2+4+3sin(a x+b)-2x=0 has at least one solution, then the value of (a+b) can be (a) (7pi)/2 (b) (5pi)/2 (c) (9pi)/2 (d) none of these

x^2 + 4 + 3 cos(ax+b) = 2x has atleast on solution then the value of a+b is :

If 4a+2b+c=0 , then the equation 3ax^(2)+2bx+c=0 has at least one real lying in the interval

0 le a le 3, 0 le b le 3 and the equation, x^(2)+4+3 cos ( ax+b) = 2x has atleast one solution, then find the value of (a+b) .

If equation x^2+2x+2 + e^alpha - 2 sin beta = 0 has a real solution in x, then (where n in ZZ )