SOLUTION: How Do I tell what the answer and sign is to this. (x-5)(x+2)<0.

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Question 44814: How Do I tell what the answer and sign is to this.
(x-5)(x+2)<0.
Found 2 solutions by adamchapman, Nate:
Answer by adamchapman(301) About Me  (Show Source):
You can put this solution on YOUR website!
%28x-5%29%28x%2B2%29%3C0
Find the values where (x-5)(x+2)=0.
The answer is when x=-2 or x=5.
If you expand the brackets using FOIL; you get:
x%5E2-3x-10%3C0
in a qaudratic equation, if the amount of x%5E2 is positive (>0), the graph of that function has a 'smiley' shape. if the amount of x-squared's is negative (<0), the graph has a 'frown' shape:
x%5E2%2Bx%2B1 is happy:
+graph%28+300%2C+200%2C+-6%2C+5%2C+-2%2C+10%2C+x%5E2%2Bx%2B1%29+
-x%5E2%2Bx%2B1 is frowning:
+graph%28+300%2C+200%2C+-6%2C+5%2C+-10%2C+2%2C+-x%5E2%2Bx%2B1%29+
If we condider the graph of our function y=x%5E2-3x-10, we can see from the amount of x%5E2's that it is a 'happy' graph. The value of y is greater as we move out from the minimum point of the graph. We know that y=0 when x=-2 and x=5, and because of it's 'happy' shape, we can deduce that the function is <0 between these values of x.
So x%5E2-3x-10%3C0 when -2 Check this with the graph of y=x%5E2-3x-10:
+graph%28+300%2C+200%2C+-4%2C+10%2C+-12%2C+5%2C+x%5E2-3x-10%29+
I hope this helps.
P.S. In am currently constructing my own online tutoring website. I would be extremely grateful if you would e-mail me some feedback on the help you received to adam.chapman@student.manchester.ac.uk
Adam

Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
(x - 5)(x + 2) < 0
x^2 - 3x - 10 < 0
+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x%5E2+-+3x+-+10%2C+0%29+
<---(-2)===(5)--->