SOLUTION: Solve the inequality. 2x^2 + 5x + 2≤ 0

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Question 869916: Solve the inequality.
2x^2 + 5x + 2≤ 0
Found 2 solutions by Fombitz, josgarithmetic:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
%28x%2B2%29%282x%2B1%29%3C=0
Break up the number line into 3 regions.
x%3C-2
-2%3Cx%3C-1%2F2
x%3E-1%2F2
Test the inequality in each region with a point.
x%3C-2, x=-3, %28-3%2B2%29%282%28-3%29%2B1%29%3C=0,%28-1%29%28-5%29%3C=0,5%3C=0 False
-2%3Cx%3C-1%2F2,x=-1,%28-1%2B2%29%282%28-1%29%2B1%29%3C=0,%281%29%28-1%29%3C=0,-1%3C=0 True
x%3E-1%2F2,x=0,%280%2B2%29%282%280%29%2B1%29%3C=0,2%3C=0, False
So the only region where the inequality is true is,
highlight%28-2%3C=x%3C=-1%2F2%29

Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
The roots of the quadratic expression are critical points. The orientation judged from the quadratic expression indicates that the inequality is satisfied for x between the critical points.

%282x%2B1%29%28x%2B2%29=0 for x=-2 or x=-1.

ThisQuadratic%3C=0 for -2%3C=x%3C=-1.