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

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

Text Solution

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The correct Answer is:
D
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Knowledge Check

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

    A
    `x^(3)-6x^(2)+216=0`
    B
    `x^(3)-3x^(2)+112=0`
    C
    `x^(3)+6x^(2)-216=0`
    D
    `x^(3)+3x^(2)-112=0`

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

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