(x-a)(x-b) - k = (x-c)(x-d) (according to Q)
(x-c)(x-d) + k = (x-a)(x-b)
so its roots are a,b
Some very easy quad sums , hope everyone gives a different process -------------
1 > If ( x - a ) ( x - b ) = k has the roots c , d ; then roots of the eqn. ( x - c ) ( x - d ) + k = 0 are --
(x-a)(x-b) - k = (x-c)(x-d) (according to Q)
(x-c)(x-d) + k = (x-a)(x-b)
so its roots are a,b