If c and d are the roots of ( x − a)( x −b) − k = 0 then the roots of ( x −c)( x − d ) + k = 0 are

$$\begin{gathered} (x-a)(x-b) -k = 0 \\ {x}^2-(a+b)x+(ab-k)=0 \\ c+d=+(a+b), cd=(ab-k)\cdots \left(1\right) \\ (x-c)(x-d)+k \\ {x}^2-(c+d)x+cd+k=0 \\ from \left(1\right) x^2-(a+b)x+ab=0 \\ (x-a)(x-b) = 0 \\ \therefore a, b are roots \end{gathered}$$