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α and β are roots, then equation is (x -α)(x -β)=0
so,if c and d are roots, then equation will be  (x -c)(x -d)=0
but,here c and d are roots of the equation (x -a)(x -b) -k =0
so, (x -c)(x -d)= (x -a)(x -b) -k 
⇒(x -c)(x -d) + k = (x -a)(x -b)_______(1)
∵  a and b are roots of equation (x -a)(x -b)=0 
and from equation (1) 
(x -c)(x -d) + k = (x -a)(x -b)
hence , a and b are roots of equation (x -c)(x -d) + k =0
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