## Quant Question Of The Day: 71

# Algebra

For how many integers ‘a’ is at least one root of the equation x³ – ax + a + 11 = 0 is a positive integer?

i) 0

ii) 2

iii) 4

iv) 5

v) More than 5

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

For how many integers ‘a’ is at least one root of the equation x³ – ax + a + 11 = 0 is a positive integer?

i) 0

ii) 2

iii) 4

iv) 5

v) More than 5

a = (x³ + 11)/(x – 1)

a is integer means (x³ + 11)/(x – 1) is integer

Now, (x³+ 11) when divided by (x – 1), remainder is (-1)³ + 11 or 12

=> 12 is divisible by (x – 1)

=> x can be 2, 3, 4, 5, 7 and 13

For x = 2 and 3, a is 19 for rest all x it will take different value

=> a can take 5 different values.

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Ans: 5