Home
Class 12
MATHS
If equation 2x^(3)-6x+2sina+3=0,a in (0,...

If equation `2x^(3)-6x+2sina+3=0,a in (0,pi)` has only one real root, then the largest interval in which a lies is

A

`(0,(pi)/(6))`

B

`((pi)/(6),(pi)/(3))`

C

`((pi)/(6),(5pi)/(6))`

D

`((5pi)/(6),pi)`

Text Solution

Verified by Experts

The correct Answer is:
C
Let `f(x)=2x^(3)-6x+2sin a+3`
`rArr" "f'(x)=6x^(2)-6=0 rArr x =pm 1`
Since equation f(x) = 0 has only one real root ltbtgt `f(-1),f(1)gt0`
`rArr" "(2sin a+7)(2sin a-1)gt0`
`rArr" "sina gt(1)/(2)rArr a in ((pi)/(6),(5pi)/(6))`
Promotional Banner

Topper's Solved these Questions

  • MONOTONOCITY AND NAXINA-MINIMA OF FUNCTIONS

    CENGAGE|Exercise Multiple Correct Answer Type|10 Videos

  • MONOTONOCITY AND NAXINA-MINIMA OF FUNCTIONS

    CENGAGE|Exercise Comprehension Type|6 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE|Exercise JEE Advanced Previous Year|17 Videos

  • PAIR OF STRAIGHT LINES

    CENGAGE|Exercise Exercise (Numerical)|5 Videos

Similar Questions

Explore conceptually related problems

If the equation has no real root, then lamda lies in the interval

If the equation 4x^(3)+5x+k=0(k in R) has a negative real root then

For all ' x^(prime),x^2+2a x+(10-3a)>0, then the interval in which ' a ' lies is

If the equation x^4- λx^2+9=0 has four real and distinct roots, then lamda lies in the interval

If the equation x^2=a x+b=0 has distinct real roots and x^2+a|x|+b=0 has only one real root, then which of the following is true? b=0, a >0 b. b=0, a 0, a >0

If z^3+(3+2i)z+(-1+i a)=0 has one real root, then the value of a lies in the interval (a in R) a. (-2,1) b. (-1,0) c. (0,1) d. (-2,3)

Without actually solving show that the equation x^(4)+2x^(3)-2=0 has only one real root in the interval (0,1) .

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)

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 .

The equation (cosp-1)x^2+(cos p)x+sin p=0 in the variable x has real roots. The p can take any value in the interval (a) (0,2pi) (b) (-pi,0) (c) (-pi/2,pi/2) (d) (0,pi)