AP ICET 2nd May 2018 Shift-2

Question 83

The number of natural numbers k such that $$\frac{3k^2 + 4k + 12}{k}$$ is a prime is

Solution

For the result to be prime, the expression must firstly yield a whole number. 
The expression can be broken up as =  3*k + 4 + (12/k)

Hence, k has to be a whole number factor of 12.
Probable values of k = 1,2,3,4,6,12 
Of these, the values of k = 1,3,4,12 yield prime numbers for the expression. 


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