If c, d are the roots of the equation (x – a) (x – b) – k = 0, then the roots of the equation (x – c) (x – d) + k = 0 are

we have,⇒ x2−(a+b)x+ab−k=0⇒ x2−(a+b)x+ab−k=0----1Since the roots of Eq. (1) are c and d∴c+d=a+b,----2and  cd=ab−k---3Now, (x−c)(x−d)+k=0⇒x2−(c+d)x+cd+k=0⇒x2−(a+b)x+ab=0[Putting the values of a + b and ab from Eqs (2) and (3)] ⇒ (x−a)(x−b)=0⇒x=a,b