TS ICET 24 May 2018 Shift 1 Paper

Question : 83 of 200

Marks: +1, -0

The number of natural numbers n such that

{4\n^2+5\n+10}/\n

is a prime number

Solution:

Given,

{4\n^2+5\n+10}/n

is prime

⇒ 4 n+5+\;{10}/{n}

is a prime
n has to be a factor of 10 to have

4 n+5+\;{10}/{n}

as an integer.
n = 1 is the only natural number satisfying the conditions.

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