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If alpha,beta,gamma are the roots of x^3...

If `alpha,beta,gamma` are the roots of `x^3-2x^2+3x-4=0` then the value of `alpha^2beta^2+beta^2 gamma^2+gamma^2alpha^2` is

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Knowledge Check

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

    A
    `-7`
    B
    `-5`
    C
    `-3`
    D
    0

  • If alpha, beta, gamma are the roots of x^3+a x^2+b=0 then the value of [[alpha , beta , gamma],[beta , gamma , alpha],[gamma , alpha , beta]] is

    A
    `- a^3`
    B
    `a^3-3 b `
    C
    `a^3`
    D
    `a^2-3 b`

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

    A
    12
    B
    13
    C
    14
    D
    15

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    If alpha , beta , gamma are the roots of x^3 + 2x^2 + 3x +8=0 then ( alpha + beta ) ( beta + gamma) ( gamma + alpha ) =

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

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