Question

HELP NEEDED IMMEDIATELY! I'M GETTING DESPERATE!

Answer 1

Answer:

The number of different possible values are {-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7}.

Step-by-step explanation:

Given : For an integer n, the inequality  $\[x^2 + nx + 15 < 0\]$  has no real solutions in x.

To find : The number of different possible values of n ?

Solution :

The given inequality is   $\[x^2 + nx + 15 < 0\]$ have no solution then the discriminant must be less than zero.

i.e. $b^2-4ac$

Here, a=1, b=n and c=15

${n}^{2} - 4 \times 1 \times 15 \: < \: 0$

${n}^{2} - 60 \: < \: 0$  

$n^2$

$n$

$n$

i.e. $- 7.75 \: < \: n \: < \: 7.75$

The integer values are {-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7}.