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If (alpha+beta) and (alpha- sqrt(beta)) ...

If `(alpha+beta) and (alpha- sqrt(beta))` ar the roots of the equation `x^(2)+px+q=0` where `alpha, beta, p and q` are real, then the roots of the equation `(p^(2)-4q)(p^(2)x^(2)+4px)-16q=0` are

A

`((1)/(alpha)+(1)/(sqrt(beta))) and ((1)/(alpha)-(1)/(sqrt(beta)))`

B

`((1)/(sqrt(alpha))+(1)/(beta)) and ((1)/(sqrt(alpha))-(1)/(beta))`

C

`((1)/(sqrt(alpha))+(1)/(sqrt(beta))) and ((1)/(sqrt(alpha))-(1)/(sqrt(beta)))`

D

`(sqrt(alpha)+ sqrt(b) and (sqrt(alpha)- sqrt(beta))`

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IF alphapmsqrtbeta be the roots of the equation x^2+px+q=0 , prove that 1/alphapm1/sqrtbeta will be the roots of the equation (p^2-4q)(p^2x^2+4px)-16q=0 .

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Knowledge Check

  • If (alpha+sqrtbeta) and (alpha-sqrtbeta) are the roots of the equation x^2+px+q=0 where alpha,beta ,p and q are real, then the roots of the equation (p^2-4q)(p^2x^2+4px)-16q =0 are

    A
    `(1/alpha+1/sqrtbeta) and (1/alpha-1/sqrtbeta)`
    B
    `(1/sqrtalpha+1/beta) and (1/sqrtalpha-1/beta)`
    C
    `(1/sqrtalpha+1/sqrtbeta) and (1/sqrtalpha-1/sqrtbeta)`
    D
    `(sqrtalpha+sqrtbeta) and (sqrtalpha-sqrtbeta)`

  • If , p , q are the roots of the equation x^(2)+px+q=0 , then

    A
    p=1,q=-2
    B
    p= 0 ,q = 1
    C
    `p=-2,q=0`
    D
    `p=-2,q=1`

  • If p and q are the roots of the equation x^2+px+q =0, then

    A
    p=1,q=-2
    B
    p=0,q=1
    C
    p=-2,q=0
    D
    p=-2,q=1

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