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September 20, 2014

September 20, 2014

Posted by **Devon** on Wednesday, October 14, 2009 at 5:47pm.

- Algebra -
**MathMate**, Wednesday, October 14, 2009 at 6:56pmThe given inequality is

x^3-2x^2-9x-2 ≥ -20

or

f(x)=x^3-2x^2-9x-18 ≥ 0

F(x) can be factored into (x-3)*(x-2)*(x+3) so the roots of f(x) are +3, -3 and 2.

F(x) has a positive leading coefficient, so the graph goes to -∞ on the left, and to +∞ on the right.

We can therefore deduce that for x<-3, f(x) is negative, and for x>3, f(x) is positive.

Also, since the intermediate root is x=2, we can also deduce that f(x) is non-negative between x=-3 and 2.

So the solution set for the given inequality is:

[-3,2]∪[3,∞), or alternatively,

-3≤x≤2 or x≥3.

http://img208.imageshack.us/img208/5915/1255556868.png

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