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IF alphapmsqrtbeta be the roots of the e...

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 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

  • If tanalpha and tanbeta are the roots of the equation x^2+px+q=0 (pne0) , then

    A
    `sin^2(alpha+beta)=q`
    B
    `tan(alpha+beta)=p/(q-1)`
    C
    `cos(alpha+beta)=1-q`
    D
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