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