If a, b in (0, 2) and the equation (2x^2...

If `a, b in (0, 2)` and the equation `(2x^2+5)/2 = x - 2cos(ax + b)` has at least one solution then

`pi`

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

QUADRATIC EQUATION & EXPRESSION
FIITJEE|Exercise ASSIGNMENT PROBLEMS (OBJECTIVE) Level - II|20 Videos
QUADRATIC EQUATION & EXPRESSION
FIITJEE|Exercise COMPREHENSIONS - I|3 Videos
QUADRATIC EQUATION & EXPRESSION
FIITJEE|Exercise ASSIGNMENT PROBLEMS (SUBJECTIVE) Level - II|28 Videos
PROGRESSION & SERIES
FIITJEE|Exercise NUMERICAL BASED|3 Videos
SET, RELATION & FUNCTION
FIITJEE|Exercise Exercise 3|8 Videos

Similar Questions

Explore conceptually related problems

If a, b ∈ [0,2pi] and the equation x^(2) + 4+3sin(ax+b)=2x has atleast one solution, and the least (+ve) . Value of a+b is k then,

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

If (x^(2) + 5)/(2) = x - 2 cos (m + nx) has at least one real root, the

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) .

The value of K so that the equation (K+1)sin x+2cos x=2+K has at least one solution is

The value of K so that the equation (K+1)sin x+2cos x=2+K has at least one solution.

The equation tan^(4)x-2sec^(2)x+a^(2)=0 will have at least one solution, if

Statement-1: If a, b, c in R and 2a + 3b + 6c = 0 , then the equation ax^(2) + bx + c = 0 has at least one real root in (0, 1). Statement-2: If f(x) is a polynomial which assumes both positive and negative values, then it has at least one real root.

the least value of 'a' for which the equation 2sqrt(a) sin^(2) x+sqrt(a-3) sin 2x=5+sqrt(a) has at least one solution is _______.

FIITJEE-QUADRATIC EQUATION & EXPRESSION -ASSIGNMENT PROBLEMS (OBJECTIVE) Level - I

Consider the equation x^(3)-nx+1=0, n in N, n ge 3. Then
Text Solution
|
If sin alpha, sin beta and cos alpha are in GP, then roots of x^2 + 2x...
Text Solution
|
If a, b in (0, 2) and the equation (2x^2+5)/2 = x - 2cos(ax + b) has a...
Text Solution
|
Let P(x) and Q(x) be two polynomials. If f(x) = P(x^4) + xQ(x^4) is di...
Text Solution
|
If (y^2-5y+3)(x 62+x+1)<2x for all x in R , then fin the interval in ...
Text Solution
|
The solution of the equation |x+1|^(2)-2|x+2|-26=0 is
Text Solution
|
If minimum value of f(x)=(x^(2)+2bx+2c^(2)) is greater than the maximu...
Text Solution
|
The number of real solutions (x, y, z, t) of simultaneous equations 2y...
Text Solution
|
The set of values of a for which (a - 1) x^(2) - (a + 1) x + a - 1 ...
Text Solution
|
if for all real value of x,(4x^2+1)/(64x^2-96x.sina+5)<1/32,then a li...
Text Solution
|
The number of real solutions of the equation sin (e^x)= 5^x+5^-x
Text Solution
|
The equation (x-3)^9+(x-3^2)^9+(x-3^3)^9+.....+(x-3^9)^9=0 has
Text Solution
|
The set of all real numbers x for which x^2-|x+2| +x gt 0 is
Text Solution
|
The exhaustive set of values of a for which the equation a sin(x+(pi)/...
Text Solution
|
If the roots of the equation (a)/(x+a+k)+(b)/(x+b+k)=2 are equal in ma...
Text Solution
|
The set of all x in the interval [0, pi] for which 2 sin^(2)x-3 sin x ...
Text Solution
|
Let a gt 0, b gt 0 then both roots of the equation ax^(2)+bx+c=0
Text Solution
|
The number of positive integral solutions of x^4-y^4=3789108 is 0 b. 1...
Text Solution
|
The set of values for which x^(3)+1 ge x^(2)+x is
Text Solution
|
If a ,b ,c are distinct positive numbers, then the nature of roots of ...
Text Solution
|