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For an integer n, the inequality x^2+nx +15<0 has no real solutions in x. Find the number of different possible values of n.

 Feb 20, 2020
edited by Guest  Feb 20, 2020
edited by Guest  Feb 20, 2020
edited by Guest  Feb 20, 2020
edited by Guest  Feb 20, 2020
 #1
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To ensure x has no real solutions. use the discriminant

 

b- 4ac < 0

 

n2 - 60 < 0

 

n2 < 60

 

Since n is a integer,

 

we now ask ourselves how many perfect squares that are below 60?

 

1, 4, 9, 16, 25, 36, 49.

 

There are 7 such perfect squares.

 

n can also be negative, so the answer should be 7 * 2 = 14

 Feb 20, 2020

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