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If alpha , beta , gamma are the root...

If ` alpha , beta , gamma ` are the roots of ` x^3 - 6x^2 +11 x-6=0` then find the equation whose roots are
` alpha^2 + beta^2, beta^2 + gamma^2 , gamma^2 + alpha^2`

Text Solution

Verified by Experts

The correct Answer is:
`x^3 -28x^2 + 245 x -650 =0`
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If alpha, beta,gamma are the roots of x^3-6x^2+11x-6=0 then find the equation whose roots are alpha^2+beta^2 ,beta^2+gamma^2,gamma^2+alpha^2

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Knowledge Check

  • If alpha, beta , gamma are the roots of x^(3) - 7x + 6 = 0 then the equation whose roots are (alpha - beta)^(2) , (beta - gamma)^(2) , (gamma - alpha)^(2) is

    A
    `x^(3) - 42x^(2) + 441x - 400 = 0 `
    B
    `x^(3) + 42x^(2) + 441x - 400 = 0`
    C
    `x^(3) + 28x^(2) + 245x - 650 = 0 `
    D
    ` x^(3) - 28x^(2) + 245x - 650 = 0`

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

    A
    ` x^3 -4x -1=0`
    B
    `x^3 -4x +1=0`
    C
    ` x^3 +4x -1=0`
    D
    `x^3 +4x +1=0`

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

    A
    `x^(3) + 3x^(2) + 8x + 16 + 0 `
    B
    `x^(3) + 3x^(2) + 8x - 16 = 0 `
    C
    `x^(3) + 3x^(2) - 8x - 16 = 0 `
    D
    `x^(3) - 3x^(2) + 8x + 16 = 0`

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