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For an integer , the inequality
 

 

\(x^2 + nx + 15 < 0\)

 

has no real solutions in x. Find the number of different possible values of n.

 Jul 25, 2020
 #1
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To ensure x has no real solutions. use the discriminant

 

b2 - 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

 Jul 25, 2020

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