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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.

 Feb 20, 2021
 #1
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x ( x  + 5)   =  -n

 

x^2  + 5x   +  n     =  0 

 

To have  no real  solutions.....the discriminant  must  be  <  0

 

So

 

5^2   - 4 (1) n   <   0

 

25  -  4n  <   0

 

25  <  4n

 

4n  >   25

 

n  >   25/4

 

n  >  6.25

 

So  n = 7, 8 , 9 ,10   provide  no real solutions.....so   4/10=  2/5  of a chance that the  n you select gives  no real solutions

 

cool cool cool

 Feb 20, 2021

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