+866 For an integer n, the inequality
x^2 + nx + 15 < -89 - 3x^2
has no real solutions in $x$. Find the number of different possible values of $n$.
+128578 Simplify as
4x^2 + nx + 104 < 0
Set up as an equality
4x^2 + nx + 104 = 0
This will have real solutions when
n^2 - 4 (4) (104) ≥ 0
n^2 ≥ 1664
n ≥ 40.79 or n ≤ -40.79
So....for our purposes n < 40.79 and n > -40.79
The number of possible values for n = [ -40 , 40 ] = 81 possible values
