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 $x^2 - 8x + n = 0$? Express your answer as a common fraction.
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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 $x^2 - 8x + n = 0$? Express your answer as a common fraction.
The quadratic will have no real solutions when (b2 – 4ac) < 0 (i.e., 4ac is more than b2)
None of the integers between 1 and 10 inclusive will do it. The probability is 0 (zero).
None of the intefers 11 through 16 will do it, either. The first integer that will do it is 17.
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