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If c ,d are the roots of the equation (x...

If `c ,d` are the roots of the equation `(x-a)(x-b)-k=0` , prove that a, b are roots of the equation `(x-c)(x-d)+k=0.`

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Knowledge Check

  • If c and d are roots of the equation (x-a) (x-b) - k = 0, then a, b are roots of the equation

    A
    `(x-c) (x-d) - k = 0`
    B
    `(x-c) (x-d) + k = 0`
    C
    `(x-a) (x-c) + k = 0`
    D
    `(x-b) (x-d) + k = 0`

  • If c, d are the roots of the quadratic equation (x - a) (x - b) - k = 0, then, a, b are the roots of the equation

    A
    (x - c) (x - d) - k= 0
    B
    (x + c) (x + d) -k = 0
    C
    (x - c) (x - d) + k= 0
    D
    (x + a) (x + b) + k= 0

  • If m and n are roots of the equation (x+p)(x+q)-k=0 then find the roots of the equation (x-m)(x-n)+k=0

    A
    `p and q`
    B
    `1/p and 1/q`
    C
    `-p and -q`
    D
    `p+q and p-q`

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    Let alpha,beta be the roots of the equation (x-a)(x-b)=c,c!=0 then the roots of the equation (x-alpha)(x-beta)+c=0 are :

    If alpha, beta be the roots of the equation (x-a)(x-b) + c = 0 (c ne 0) , then the roots of the equation (x-c-alpha)(x-c-beta)= c , are

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