Answer:
B
Step-by-step explanation:
A. x^2 - 2x - 8 < 0
(x - 4)(x + 2) < 0
B. x^2 + 2x - 8 < 0
(x + 4)(x - 2) < 0
C. x^2 - 2x - 8 > 0
(x - 4)(x - 2) > 0
D. x^2 + 2x - 8 > 0
(x + 4)(x - 2) > 0
Since roots here are -4 and 2, the answer is either B or D.
When you test a point in the interval between -4 and 2, for example 0, it is negative.
So the answer is B.
Answer:
The answer is [tex]x^2+2x-8<0[/tex]
Step-by-step explanation:
In order to determine the answer, we have two alternatives:
In this case, we use the second option because it is easier to replace a value and solving basic math operations. Also, if we choose a good first value, we will eliminate immediately some options.
We can choose values between -4 and 2. Every time we could choose 0 value, we should do it.
First value: [tex]x=0[/tex]. Replacing:
[tex]-8<0\\-8<0\\-8>0\\-8>0[/tex]
We can see that the two first options are correct, the two last options are wrong.
Second value: [tex]x=-3[/tex]. Replacing:
[tex](-3)^2-2*(-3)-8<0\\9+6-8<0\\7<0\\\\(-3)^2+2*(-3)-8<0\\9-6-8<0\\-5<0[/tex]
We can see that the first option is wrong.
Finally, the correct option is the second one:
[tex]x^2+2x-8<0[/tex]
