If alpha, beta, gamma are the cube roots...

If `alpha, beta, gamma` are the cube roots of a negative number p, then for any three real numbers x,y,z the value of `(x alpha+y beta+ z gamma)/(x beta +y gamma+z alpha)` is

`(1-isqrt(3))/(2)`

`(-1- isqrt(3))/(2)`

`(x+y+z)i`

`p i`

Text Solution

Verified by Experts

The correct Answer is:

Topper's Solved these Questions

COMPLEX NUMBERS AND QUADRATIC EQUATIONS
NEW JOYTHI PUBLICATION|Exercise EXERCISE|50 Videos
BINOMIAL THEOREM
NEW JOYTHI PUBLICATION|Exercise QUESTIONS FROM COMPETITIVE EXAMS|51 Videos
CONIC SECTIONS
NEW JOYTHI PUBLICATION|Exercise EXERCISE - HYPERBOLA|9 Videos

Similar Questions

Explore conceptually related problems

If alpha, beta, gamma are the roots of 9x^3 - 7x + 6 = 0 , then alpha beta gamma is …………

If alpha, beta, gamma are the roots of the equation x^3 - 3x + 11 =0 , then alpha + beta + gamma is ………….

If alpha, beta and gamma are the roots of the equation x^(3) + 3x^(2) - 24x + 1 = 0 thebn find the value of (3sqrt(alpha)+3sqrt(beta)+ 3sqrt(gamma)).

If alpha , beta, gamma are the roots of the equation x^3-4x^2+3x-1=0 , then the equation whose roots are (alpha+beta+gamma), alphabetagamma is :

If alpha,beta,gamma are the roots of the equation x^3-p x+q=0, then find the cubic equation whose roots are alpha/(1+alpha),beta/(1+beta),gamma/(1+gamma) .

If alpha,beta,gamma are the roots of the equation x^3+4x+1=0, then find the value of (alpha+beta)^(-1)+(beta+gamma)^(-1)+(gamma+alpha)^(-1) .

If alpha, beta and gamma are the roots of the cubic equation x^3 + 2x^2 + 3x + 4 = 0, for a cubic equation roots are 2 alpha, 2 beta, 2 gamma

If alpha, beta , gamma are the roots of the equation x^3-3x+2=0 then the equation whose roots are 1/alpha,1/beta,1/gamma is :

Let alpha ,beta and gamma be the roots of the equations x^(3) +ax^(2)+bx+ c=0,(a ne 0) . If the system of equations alphax + betay+gammaz=0 beta x +gamma y+ alphaz =0 and gamma x =alpha y + betaz =0 has non-trivial solution then

NEW JOYTHI PUBLICATION-COMPLEX NUMBERS AND QUADRATIC EQUATIONS-QUESTIONS FROM COMPETITIVE EXAMS

Let z=(11-3i)/(1+i). If alpha is a real number such z-ialpha is real, ...
Text Solution
|
Let z(1)" and "z(2) be the roots of the equation z^(2)+pz+q=0, where p...
Text Solution
|
If alpha, beta, gamma are the cube roots of a negative number p, then ...
Text Solution
|
The magnitude and amplitude of ((1+isqrt(3))(2+2i))/((sqrt(3)-i)) are ...
Text Solution
|
If 1+x^(2)=sqrt(3)x, then sum(n=1)^(24)(x^(n)-(1)/(x^n))^(2) is equal ...
Text Solution
|
If alpha and beta are the roots of the equation ax^(2)+bx+c=0 then (a...
Text Solution
|
If one root of the equation x^(2)+px+12=0 is 4, while the equation x^(...
Text Solution
|
Given tan A and tan B are the roots of x^(2)-ax+b=0. The value of sin^...
Text Solution
|
The number of roots of the equation |x|= x^(2)+x-4 is
Text Solution
|
If alpha, beta are the roots of the equation x^(2)-px+q=0, prove that ...
Text Solution
|
If sec alpha" and cosec "alpha are the roots of the equation x^(2)-px+...
Text Solution
|
Let a(n)=i^((n+1)^2), where i=sqrt(-1)" and "n=1, 2, 3,"………..". Then t...
Text Solution
|
If (5z2)/(11z1) is purely imaginary, then the value of |(2z(1)+3z(2))/...
Text Solution
|
If 2alpha= -1-isqrt(3)" and"2beta= -1+isqrt(3), then 5alpha^(4)+5beta^...
Text Solution
|
If (i^(4)+i^(9)+i^(16))/(2-i^(8)+i^(10)+i^(3))=a +ib, then (a,b) is
Text Solution
|
If (sqrt(5)+sqrt(3)i)^(33)= 2^(49)z, then modulus of the complex numbe...
Text Solution
|
If a is positive and if A and G are the arithmetic mean and the geomet...
Text Solution
|
Suppose that two persons A and B solve the equation x^(2)+ax+b=0. Whil...
Text Solution
|
If alpha, beta are the roots of the equation x^(2)+x+1=0, then the equ...
Text Solution
|
If sec theta" and "tan theta are the roots of ax^(2)+bx+c=0 (a,b ne 0)...
Text Solution
|