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If alpha and beta are roots of the quadr...

If `alpha and beta` are roots of the quadratic equation `x ^(2) + 4x +3=0,` then the equation whose roots are `2 alpha + beta and alpha + 2 beta` is :

A

`x ^(2) -12x +35=0`

B

`x ^(2)+ 12x-33 =0`

C

`x ^(2) -12x-33=0`

D

`x ^(2) +12x+35=0`

Text Solution

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The correct Answer is:
D
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Knowledge Check

  • If alpha and beta are the roots of the quadratic equation x^2+4x+3=0 , then the equation, whose roots are 2alpha+beta and alpha+2beta , is

    A
    `x^2-12x+35=0`
    B
    `x^2+12x-35=0`
    C
    `x^2-12x-35=0`
    D
    `x^2+12x+35=0`

  • If alpha and beta are the roots of the quadratic equation x^2+x+1=0 , then the equation, whose roots are alpha^(19) and beta^(7) , is

    A
    `x^2-x-1=0`
    B
    `x^2-x-1=0`
    C
    `x^2+x-1=0`
    D
    `x^2+x+1=0`

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

    A
    `x^(2) + x + 1 = 0`
    B
    `x^(2) - x + 1 = 0`
    C
    `x^(2) - x - 1 = 0`
    D
    `x^(2) + x - 1 = 0`

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