Home
Class 12
MATHS
If the equation a sin^(3)x+(b-s)sin^(2)x...

If the equation `a sin^(3)x+(b-s)sin^(2)x+(c-b)sin x=c =0` has exactly three distinct solutions in `[0, pi]`, where a + b + c = 0, then which of the following is not the possible value of c/a ?

A

1

B

`(1)/(4)`

C

`(sqrt(2))/(7)`

D

`(2)/(7)`

Text Solution

Verified by Experts

The correct Answer is:
A
`a sin^(3)x + (b-a)sin^(2)x + (c-b)sin x-c=0`
`rArr (sin x-1)(a sin^(2)x + b sin x + c)=0`
Also a + b + c = 0
`therefore` one of the solutions of the equation `a sin^(2) x + b sin x + c = 0`
is sin x = 1
Product of roots = x/a ltbRgt For three solutions, we must have `0 le (c )/(a) lt 1`
Promotional Banner

Similar Questions

Explore conceptually related problems

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 the equation |sin x |^(2) + |sin x|+b =0 has two distinct roots in [0, pi][ then the number of integers in the range of b is equal to:

In triangle ABC , B = pi/3 and sin A : sin c = x then find the set of all possible values of x.

If the equation sin^(2)x-a sin x+b=0 has only one solution in (0,pi) then which of the following statements are correct?

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

Let cos A+cos B+cos C=0 and sin A+sin B+sin C=0 then which of the following statement(s) is/are correct?

Show that: sin A sin(B-C)+sin B sin(C-A)+sin C sin(A-B)=0

If the roots of the equation c^(2)x^(2)- c(a+b)x + ab =0 are sin A, sin B where A, B and C are the angles and a, b, c are the opposite sides of a triangle, then the triangle is : (i) right angled (ii) acute angled (iii) obtuse angled (iv) sin A + cos A = (a+b)/(c )