HELP NEEDED IMMEDIATELY! I’M GETTING DESPERATE! For an integer $n$, the inequality \[x^2 + nx + 15 < 0\]has no re

Question

HELP NEEDED IMMEDIATELY! I’M GETTING DESPERATE!

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 $n$.

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Ariana 4 weeks 2021-09-19T08:18:08+00:00 1 Answer 0

Answers ( )

    0
    2021-09-19T08:20:00+00:00

    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<0

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

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

    {n}^{2}  - 60  \: <  \: 0  

    n^2<60

    n<\pm \sqrt{60}

    n<\pm 7.75

    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}.

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45:7+7-4:2-5:5*4+35:2 =? ( )