Quant Question Of The Day: 78
Algebra
The roots of the quadratic equation x² – nx + 2n = 0 are integers. What is the sum of all possible values of n ?
A. 16
B. 17
C. 18
D. None of the above
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.
B.17
How is the answer 17?
Correct answer is 16.
See the answer’s explanation here : https://tathagat.mba/quant-question-of-the-day-78/