Let alpha,beta,gamma be the roots of x^(...

Let `alpha,beta,gamma` be the roots of `x^(3)+x+10=0` and `alpha_(1)=(alpha+beta)/(gamma^(2)),beta_(1)=(beta+gamma)/(alpha^(2)),gamma_(1)=(gamma+alpha)/(beta^(2))`. Then, the value of `(alpha_(1)^(3)+beta_(1)^(3)+gamma_(1)^(3))-(1)/(10)(alpha_(1)^(2)+beta_(1)^(2)+gamma_(1)^(2))` is

A

`(1)/(10)`

B

`(1)/(5)`

C

`(3)/(10)`

D

`(1)/(2)`

Text Solution

Verified by Experts

The correct Answer is:

3

Promotional Banner

Promotional Banner

Topper's Solved these Questions

THEORY OF EQUATIONS
DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 1B|76 Videos
THEORY OF EQUATIONS
DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 2 (SPECIAL TYPE QUESTIONS) SET -1|5 Videos
THEORY OF EQUATIONS
DIPTI PUBLICATION ( AP EAMET)|Exercise SET - 4|4 Videos
THEORETICAL DISTRIBUTIONS
DIPTI PUBLICATION ( AP EAMET)|Exercise EXERCISE 2 (SPECIAL TYPE QUESTIONS) CHOOSE THE CORRECT ANSWER FROM THE ALTERNATIVES 1.2.3 OR 4 GIVEN (SET -4)|5 Videos
TRANSFORMATION OF AXES
DIPTI PUBLICATION ( AP EAMET)|Exercise SET-4|3 Videos

Similar Questions

Explore conceptually related problems

If alpha , beta , gamma are the roots of 2x^3 -2x -1=0 the sum ( alpha beta)^2 =

If alpha , beta , gamma are the roots of x^3 + qx +r=0 then (1)/( alpha + beta - gamma) +(1)/( beta + gamma - alpha) +(1)/(gamma + alpha - beta) =

If alpha , beta , gamma are the roots of x^3 +2x^2 -3x -1=0 then alpha^(-2) + beta^(-2) + gamma^(-2)=

If alpha, beta, gamma are the roots of x^(3) + x^(2) + x + 1 = 0 then alpha^(2) + beta^(2) + gamma^(2) =

If alpha, beta, gamma are the roots of x^(3) + x^(2) + x + 1 =0 then alpha^(4) + beta^(4) + gamma^(4) =

If alpha, beta, gamma are the roots of x^(3)+px+q=0 then |(alpha, beta, gamma),(beta, gamma, alpha),(gamma, alpha, beta)|=

If alpha, beta ,gamma are the roots of x^(3) + x^(2) + x + 1 = 0 then alpha^(3) + beta^(3) + gamma^(3) =

Suppose alpha, beta, gamma are the roots of x^(3)+x^(2)+x+2=0 . Then the value of ((alpha+beta-2gamma)/(gamma))((beta+gamma-2alpha)/(alpha))((gamma+alpha-2beta)/(beta)) is

DIPTI PUBLICATION ( AP EAMET)-THEORY OF EQUATIONS-EXERCISE 1A

If alpha, beta,gamma are roots of x^(3) - px^(2) + qx - r = 0 then su...
Text Solution
|
If alpha, beta, gamma are roots of x^(3) - px^(2) + qx - r = 0 then s...
Text Solution
|
If alpha, beta,gamma are roots of x^(3) - px^(2) + qx - r = 0 then al...
Text Solution
|
If alpha, beta, gamma are roots of x^(3) - px^(2) + qx - r = 0 then (...
Text Solution
|
If alpha, beta, gamma are roots of x^(3) - 2x^(2) + 3x - 4 = 0, then ...
Text Solution
|
If alpha, beta, gamma are roots of the equation 3x^(3) + 6x^(2) - 9x...
Text Solution
|
If alpha, beta, gamma are roots of x^(3) - 2x^(2) + 3x - 4 = 0, then ...
Text Solution
|
If alpha, beta, gamma are roots of the equation x^(3) - 6x^(2) + 11x...
Text Solution
|
Suppose alpha, beta, gamma are the roots of x^(3)+x^(2)+x+2=0. Then th...
Text Solution
|
If alpha, beta, gamma are roots of x^(3) + ax^(2) + bx + c = 0 then su...
Text Solution
|
If alpha, beta, gamma are roots of x^(3) - ax^(2) + bx + c = 0 then (...
Text Solution
|
If alpha, beta, gamma are roots of the equation x^(3) - px^(2) + qx - ...
Text Solution
|
If alpha, beta, gamma,delta are roots of x^(4) - 4x^(2) - x + 2 = 0 t...
Text Solution
|
If alpha1 , alpha2 ,……….,alphan are the roots of x^n + px + q = 0 , ...
Text Solution
|
If alpha1 , alpha2 ,……….,alphan are the roots of x^n + px + q = 0 , ...
Text Solution
|
if (5x^(2) +2)/(x^(3)+x)=(A(1))/(x)+(A(2)x+A(3))/(x^(2)+1), then (A(...
Text Solution
|
If alpha, beta, gamma are roots of equation x^(3) - 10x^(2) + 7x + 8 ...
Text Solution
|
Let alpha,beta,gamma be the roots of x^(3)+x+10=0 and alpha(1)=(alpha+...
Text Solution
|
The real number k for which the equation, 2x^(3) + 3x + k = 0 has two ...
Text Solution
|
The number of real roots of the equation x^(5) + 3x^(3) + 4x + 30 = 0 ...
Text Solution
|