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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 + 1) = n ? Express your answer as a common fraction.

 Dec 13, 2020
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There are only 2 integers for n that give solution to the equation:

 

And that is when n = 2  and  n = 6

 

Therefore, the probability that your n has no solution is: 8 / 10 = 4 / 5

 Dec 13, 2020

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