For an integer , the inequality
\(x^2 + nx + 15 < 0\)
has no real solutions in x. Find the number of different possible values of n.
To ensure x has no real solutions. use the discriminant
b2 - 4ac < 0
n2 - 60 < 0
n2 < 60
Since n is a integer,
we now ask ourselves how many perfect squares that are below 60?
1, 4, 9, 16, 25, 36, 49.
There are 7 such perfect squares.
n can also be negative, so the answer should be 7 * 2 = 14
