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.
+2272
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.
x(x + 8) = –n
x2 + 8x = –n
x2 + 8x + n = 0
For there to be no real solutions, the discriminant has to be negative.
b2 – 4ac < 0
82 – (4)(1)(n) < 0
64 – 4n < 0
If n is anything larger than 16, there is no real solution.
If n is anything less than 16, there are two solutions for x.
So the probability that any number between 1 and 10 will
result in no real solution is 0 ... that's a zero.
.
