I choose a random integer n between 1 and 10 inclusive. What is the probability that for the n I chose, there exist no real solutions to the equation \(x(x + 8) = -n\)? Express your answer as a common fraction.
+128408 Let's write the equation as
x^2 + 8x + n = 0
We will only have no real solutions whenever the discriminant is < 0
So
8^2 - 4(1)(n) < 0
64 < 4n
4n > 64
n > 16
In other words, we will have real solutions for any integer n from 1 - 10 inclusive
So......the probability is 0
