Question

The sum of all possible values of n, where n is an integer when 4n2 + 6n + 8 is divided by 2n gives an integer, is

Answer 1

Answer:

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Answer 2

Given : 4n² + 6n + 8 is divided by 2n gives an integer

To find : sum of all possible values of n

Solution:

4n²  + 6n   +  8 is divisible by 2n

2n  _|  4n²  + 6n   +  8  |_   2n  + 3

          4n²

         _____

                 6n  + 8

                 6n

                ________

                           8

8 must be divisible by 2n      

8 is divisible by 2 , 4 or  8  

2n = 2  , 4 , 8

=> n = 1  ,  2  ,  4  

Possible values of n =  1 , 2  , 4  

Sum = 1 + 2 + 4  =  7

or simply 4n²  + 6n   +  8  = 2n(2n + 3)  +  8  hence 8 must be divisible by 2n

sum of all possible values of n = 7

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