Posted by Devon on Wednesday, October 14, 2009 at 5:47pm.
x^32x^29x2 is greater than or equal to 20. I got (9+x^2)(x2)(x2). That would mean for the first grouping, the answer would be 3 or 3. My book listed them separately. Could I instead go +/ 3? I then got double root of two. But my book says the other answer is infinity. Where's that come from? Thanks!!!!!!!!!

Algebra  MathMate, Wednesday, October 14, 2009 at 6:56pm
The given inequality is
x^32x^29x2 ≥ 20
or
f(x)=x^32x^29x18 ≥ 0
F(x) can be factored into (x3)*(x2)*(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 nonnegative 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.
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