If alpha is the only real root of the eq...

If `alpha` is the only real root of the equation `x^(3) + bx^(2) + cx + 1 = 0 (b lt c)`, then find the value of `tan^(-1) alpha + tan^(-1) (alpha^(-1))`

`-pi`

`- pi/2`

`pi/2`

`pi`

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

INVERSE TRIGONOMETRIC FUNCTIONS
ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|20 Videos
INVERSE TRIGONOMETRIC FUNCTIONS
ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|14 Videos
INVERSE TRIGONOMETRIC FUNCTIONS
ARIHANT MATHS|Exercise Exercise For Session 7|7 Videos
INDEFINITE INTEGRAL
ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|8 Videos
LIMITS
ARIHANT MATHS|Exercise Exercise For Session 6|5 Videos

Similar Questions

Explore conceptually related problems

If alpha " and " beta ( alpha gt beta) are roots of the equation x^(2) - sqrt2 x + sqrt( 3 - 2 sqrt 2 ) = 0", then the value of " ( cos^(-1) alpha + tan^(-1) alpha + tan ^(-1) beta) is equal to

If tan "" (alpha )/(2) and tan "" (beta)/( 2) are the roots of the equation 8x ^(2) -26x + 15 =0, then find the value of cos (alpha + beta).

If alpha, beta gamma are the real roots of the equation x^(3)-3px^(2)+3qx-1=0 , then find the centroid of the triangle whose vertices are (alpha, (1)/(alpha)), (beta, (1)/(beta)) and (gamma, (1)/(gamma)) .

If alpha and beta (alpha lt beta) are the roots of the equation x^(2) + bx + c = 0 , where c lt 0 lt b , then

If alpha and beta is the root of the equation x^2-3x+2=0 then find the value of alpha^2 + beta^2

If alpha and beta is the root of the equation x^2-3x+2=0 then find the value of alpha^2 + beta^2 + 2alphabeta

If alpha, beta are the roots of the equation : 2x^2-2(1+n^2)x+(1+n^2+n^4)=0 , then what is the value of alpha^2 + beta^2 ?

If alpha,beta be the roots of the equation 3x^2+2x+1=0, then find value of ((1-alpha)/(1+alpha))^3+((1-beta)/(1+beta))^3

If alpha and beta are the roots of the equation ax^2 + bx +c =0 (a != 0; a, b,c being different), then (1+ alpha + alpha^2) (1+ beta+ beta^2) =

If alpha and beta are the complex roots of the equation (1+i)x^(2)+(1-i)x-2i=0 where i=sqrt(-1) , the value of |alpha-beta|^(2) is

ARIHANT MATHS-INVERSE TRIGONOMETRIC FUNCTIONS-Exercise (Single Option Correct Type Questions)

The value of alpha such that sin^(-1)2/(sqrt(5)),sin^(-1)3/(sqrt(10)),...
Text Solution
|
Prove that (cos^3x - sin^3x)/(cosx - sinx) = (2 + sin2x)/2
Text Solution
|
If alpha is the only real root of the equation x^(3) + bx^(2) + cx + 1...
Text Solution
|
Let u = cot^(-1) sqrt(cos 2 theta) - tan^(-1) sqrt( cos 2 theta) , ...
Text Solution
|
Let f(x)= cos^(-1) ((1-x^2)/(1+x^2))= 2 tan^(-1)x x ge 0 , =-2 tan^(-1...
Text Solution
|
Let f(x)= sin^(-1)((2x)/(1+x^2))AAx in R. The function f(x) is continu...
Text Solution
|
Let f: Rvec[0,pi/2) be defined by f(x)=tan^(-1)(x^2+x+a)dot Then the s...
Text Solution
|
Let f(x)=sin^(-1)2x + cos^(-1)2x + sec^(-1)2x. Then the sum of the max...
Text Solution
|
If tan^(-1) . b/(c+a) + tan^(-1) . (c)/(a + b) = pi/4where a, b, c , a...
Text Solution
|
Solutions of sin^(-1) (sinx) = sinx are if x in (0, 2pi)
Text Solution
|
The equation e^(sin^(-1)x)/pi=y/(log y) has
Text Solution
|
Let f(x) =1+2sin(e^x/(e^x+1)) x ge 0 then f^(-1)(x) is equal to (assu...
Text Solution
|
cos^(-1) (cos (2 cot^(-1) (sqrt2 -1))) is equal to
Text Solution
|
The maximum value of f(x)=tan^(-1)(((sqrt(12)-2)x^2)/(x^4+2x^2+3)) is
Text Solution
|
If tan^(-1)(sqrt(1+x^2-1))/x=4^0 then x=tan2^0 (b) x=tan4^0 x=tan1/4...
Text Solution
|
If tan^(-1)(sin^2theta-2sintheta+3)+cot^(-1)(5^sec^(2y)+1)=pi/2, then ...
Text Solution
|
The number of solution of the equation |tan^(-1)|x||=sqrt((x^(2)+1)^(2...
Text Solution
|
For any real number x ge 1, the expression sec^(2)x ( tan^(-1)x) - ...
Text Solution
|
Let f : R to [0, pi/2) be defined by f ( x) = tan^(-1) ( x^(2) + x +...
Text Solution
|
The value of expression tan^(- 1)((sqrt(2))/2)+sin^(- 1)((sqrt(5))/5)-...
Text Solution
|