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If alpha ,beta, gamma are roots of the c...

If `alpha ,beta, gamma` are roots of the cubic equation `x^(3)+2x^(2)-x-3=0` then Area of the triangle with vertices `(alpha,beta),(beta,gamma),(gamma,alpha)` is:

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Knowledge Check

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

    A
    p
    B
    q
    C
    `p^(2)-2q`
    D
    0

  • If alpha, beta, gamma are the root of the equation x^(3)-3x+11=0 then the equation whose roots are (alpha+beta), (beta-gamma) and (gamma+alpha) is :

    A
    `x^(3)+3x+11=0`
    B
    `x^(3)-3x+11=0`
    C
    `x^(3)+3x-11=0`
    D
    `x^(3)-3x-11=0`

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    alpha , beta , gamma are the roots of the equation x^(3)-3x^(2)+6x+1=0 . Then the centroid of the triangle whose vertices are (alpha beta,1/(alpha beta)) , (beta gamma, 1/(beta gamma)) , (gamma alpha,1/(gamma alpha)) is

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