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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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Since c and d are the roots of the equation
(x-a) (x-b) - K=0, we have
(x - a)(x-b)-K = (x - c) (x - d)
or (x - a)(x-b) = (x - c) (x - d) + K
or (x - c)(x-d)+ K = (x - a) (x - b)
Clearly, a and b are roots of the equation (x - a ) (x - b) = 0 .Hence, a and b are roots of (x-c)(x-d) + k = 0
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