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I choose a random integer n between 1 and 10 inclusive. What is the probability that for the I chose, there exist no real solutions to the equation x(x + 2) = -n? Express your answer as a common fraction.

 May 8, 2021
 #1
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Rewrite  as

 

x(x + 2)  +  n =  0

 

x^2  + 2x   +  n  = 0

 

If we have no real solutions, the discriminant  is  <  0       ....so.....

 

2^2 - 4n < 0

4  - 4n < 0

4 < 4n

n >  1

 

So... no  real  solutions  exist    when  n =  [ 2, 10 ]

 

So         9 /10   proobability of no real solutions

 

 

cool cool cool

 May 8, 2021

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