Home
Class 11
MATHS
If alpha, beta and gamma are the roots o...

If `alpha, beta and gamma` are the roots of the equation `x^(3) + px + q = 0` (with `p != 0 and p != 0 and q != 0`), the value of the determinant
`|(alpha,beta,gamma),(beta,gamma,alpha),(gamma,alpha,beta)|`, is

A

p

B

q

C

`p^(2) - 2q`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
It is given that `alpha, beta, gamma` are the roots of the given equations.
`:. alpha + beta + gamma = 0`.
So,
`Delta = |(alpha,beta,gamma),(beta,gamma,alpha),(gamma,alpha,beta)|`
`Delta = |(alpha + beta + gamma,beta,gamma),(alpha + beta + gamma,gamma,alpha),(alpha + beta + gamma,alpha,beta)| " " [ " Using" C_(1) rarr C_(2) + C_(2) + C_(3)]`
`Delta = |(0,beta,gamma),(0,gamma,alpha),(0,alpha,beta)| [ :. alpha + beta + gamma = 0]`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • DETERMINANTS

    OBJECTIVE RD SHARMA|Exercise Section II - Assertion Reason Type|6 Videos

  • DETERMINANTS

    OBJECTIVE RD SHARMA|Exercise Exercise|94 Videos

  • DETERMINANTS

    OBJECTIVE RD SHARMA|Exercise Chapter Test|30 Videos

  • CONIC SECTIONS

    OBJECTIVE RD SHARMA|Exercise Section I - Solved Mcqs|1 Videos

  • DISCRETE PROBABILITY DISTRIBUTIONS

    OBJECTIVE RD SHARMA|Exercise Exercise|40 Videos

Similar Questions

Explore conceptually related problems

If alpha,beta,gamma are the roots of the equation x^(3)+px^(2)+qx+r=0 such that alpha+beta=0 then

If alpha, beta, gamma are the roots of the equation x^3 - x^2 + 4 = 0 , then form an equation where roots are (betagamma + beta + gamma)/(beta + gamma - alpha), (agamma + alpha + gamma)/(alpha + gamma - beta) , (beta alpha + beta + alpha)/(beta + alpha - gamma)

Knowledge Check

  • If alpha, beta and gamma are the roots of the equation px^(3)+qx^(2)+r=0 , then the value of the determinant |(alphabeta, beta gamma,gamma alpha),(beta gamma, gamma alpha, alphabeta),(gamma alpha, alpha beta,beta gamma)| is

    A
    pq
    B
    qr
    C
    0
    D
    pr

  • If alpha,beta and gamma are the roots of the equation x^(3)+px+q=0 , then the value of the determinant |(alpha,beta,gamma),(beta,gamma,alpha),(gamma,alpha,beta)| is

    A
    0
    B
    `-2`
    C
    2
    D
    4

  • If alpha, beta, gamma are the cube roots of 8 , then |(alpha,beta,gamma),(beta,gamma,alpha),(gamma,alpha,beta)|=

    A
    0
    B
    1
    C
    8
    D
    2

    • Similar Questions

    Explore conceptually related problems

    If alpha,beta& gamma are the roots of the equation x^(3)+px+q=0, then the value of the det[[alpha,beta,gammabeta,gamma,alphagamma,alpha,beta]] is

    If alpha,beta & gamma are the roots the equations x^(3)+px+q=0 then the value of the determinant [{:(,alpha,beta,gamma),(,beta,gamma,alpha),(,gamma,alpha,beta):}]

    If alpha, beta, gamma are the roots of x^(3) + ax^(2) + b = 0 , then the value of |(alpha,beta,gamma),(beta,gamma,alpha),(gamma,alpha,beta)| , is

    If alpha, beta, gamma are the roots of x^(3)+ax^(2)+b=0 then the determinant Delta=|(alpha, beta, gamma),(beta, gamma, alpha),(gamma, alpha, beta)| equals

    |(alpha,alpha^2,beta+gamma),(beta,beta^2 ,gamma+alpha),(gamma,gamma^2,alpha+beta)| is equal to

    Home
    Profile