If n is a +ve integer,then how many values of n will give an integral value of (16n^2+7n+6)/n ?
Answers
Answer:
(16n^2+7n+6)/n= 16n+7+6/n now here this expression will only be integral when 6/n would be an integral value, and at the same time 16n should be integral as well.
Therefore the possible values of n would be 6,3,2,1,1/2,1/4,1/8,1/16. Apart from these values either 16n or 6/n would not be integral in nature.
So, a total of 8 values.
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Answer:
✎﹏﹏﹏●‿●﹏﹏﹏✍️.
Given term is:.
(16n2 + 7n + 6)/n
Now, in order to find out the number of values of n, for whichpossess integral value, the requisite condition is that the denominator(n) should completely divide the numerator (16n2 + 7n + 6).
Now, for any value of n, it must divide the 16n2 and 7n but the divisibility of 6 by n is dependent on three values i.e., 2,3 and 6 (all three are the factors of number 6).
So, for n = 2,3 and 6 , the term
(16n2 + 7n + 6)/n
possess integral value.
Hence, there are 3 values of n for which the term
(16n2 + 7n + 6)/n
possess integral value.