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For an integer $n$, the inequality

\[x^2 + nx + 15 < 0\]has no real solutions in $x$. Find the number of different possible values of $n$.

The number of different possible values are {-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7}.

Step-by-step explanation:

Given : For an integer n, the inequality    has no real solutions in x.

To find : The number of different possible values of n ?

Solution :

The given inequality is   have no solution then the discriminant must be less than zero.

i.e.

Here, a=1, b=n and c=15

i.e.

The integer values are {-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7}.