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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 \(x(x + 8) = -n\)? Express your answer as a common fraction.

 Jun 7, 2022
 #1
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Let's write the equation as

 

x^2 + 8x  +  n  =  0

 

We will only have no real solutions  whenever the discriminant is <  0

 

So

 

8^2  - 4(1)(n)  < 0

 

64 <  4n

 

4n >  64

 

n > 16

 

In other words, we will have real solutions for  any integer  n   from 1 - 10 inclusive

 

So......the probability is  0

 

cool cool cool

 Jun 7, 2022

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