## 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

Categories:
Quant question of the day, Question of the day

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

x^{2} – 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.

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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/