Algebra

x² – nx + 2x = 0

Sum of the roots : A + B = n
Product of the roots : AB = 2n

2n = 2A + 2B

=> AB – 2A – 2B = 0

AB – 2A – 2B + 4 = 4
A ( B -2) – 2 ( B -2) = 4

(A – 2 ) ( B -2) = 4

=> (A, B) = (6,3) or (4,4) or ( 1 , -2) or (0,0)

Distinct values of n = 9 , 8 , -1 and 0 .

Sum of all distinct values of n =  9 + 8 -1 = 16.