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 [tex]\[x^2 + nx + 15 < 0\][/tex] has no real solutions in x.
To find : The number of different possible values of n ?
Solution :
The given inequality is [tex]\[x^2 + nx + 15 < 0\][/tex] have no solution then the discriminant must be less than zero.
i.e. [tex]b^2-4ac<0[/tex]
Here, a=1, b=n and c=15
[tex]{n}^{2} - 4 \times 1 \times 15 \: < \: 0[/tex]
[tex]{n}^{2} - 60 \: < \: 0[/tex]
[tex]n^2<60[/tex]
[tex]n<\pm \sqrt{60}[/tex]
[tex]n<\pm 7.75[/tex]
i.e. [tex]- 7.75 \: < \: n \: < \: 7.75[/tex]
The integer values are {-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7}.
