+1207 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+5)=−n? Express your answer as a common fraction.
x(x+5) = -n if and only if x+5 is -1. then x must be -6. The probability must be zero. :) :) :)
+130466 x(x + 5) = -n
x^2 + 5x = -n
x^2 + 5x + n = 0
This will have no real solutions when
5^2 - 4(1)n < 0
25 - 4n < 0
25 < 4n
25/4 < n this means that this will have no real solutions when
n > 6.25
So...it will have no real solutions when n = 7, 8, 9 or 10
So....the probability of no real solutions = 4 /10 = 2 / 5
