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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.

 Aug 6, 2020
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Hint, you shouldn't be lazy and let other people do the work for you, mathematicions like Albert Einstein took years to figure out one question.
 

anyways, you should simplify x(x+5)=-n which will be x^2+5x+n=0, then make a chart with two columns and 10 rows and you plug in 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 into x^2+5x+n=0, then if the discriminant (b^2-4ac) is negative, it has unreal roots, 

 

I'll do one for you, for example if we have 7 as n, then 

a=1

b=5

c=7

then plug these into b^2-4ac and you will get (5)^2 -- (4)(1)(7), this will equal to 

25-28 which is [-3] this means that if n is 7, then the quadratic has no real roots, if b^2-4ac is equal to something positive then it has real roots.

 Aug 6, 2020

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