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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 $x(x+5) = -n$? Express your answer as a common fraction.

 Mar 16, 2019
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\(x(x+5) = -n\\ x^2 + 5x +n =0\\ \text{no real roots if discriminant is negative}\\ D = 25-4n\\ D < 0 \Rightarrow n \geq 7\\ P[n \geq 7] = \dfrac{4}{10} = \dfrac{2}{5}\)

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 Mar 16, 2019

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