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
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 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