+0  
 
0
5
1
avatar+940 

For an integer n, the inequality
x^2 + nx + 15 < -89 - 3x^2
has no real solutions in $x$.  Find the number of different possible values of $n$.

 Apr 23, 2024
 #1
avatar+128772 
+1

Simplify as

 

4x^2 + nx + 104 <  0

 

Set up as an equality

 

4x^2 + nx + 104 =  0

 

This will have real solutions when

 

n^2  - 4 (4) (104) ≥  0

 

n^2 ≥ 1664

 

n ≥ 40.79            or   n  ≤ -40.79

 

So....for our purposes   n < 40.79     and  n > -40.79

 

The number of  possible values for n  =  [ -40 , 40 ] =   81 possible values

 

cool cool cool

 Apr 23, 2024

2 Online Users

avatar
avatar