Actually, your equation
x³+2x²+x≥0
is a cubic equation, since the highestorder term is x³. Fortunately, we can easily factor out an overall x,
x(x²+2x+1) ≥0,
and write the quadratic term as a complete square:
x(x+1)² ≥0.
How can the lefthand side be nonnegative (which is what "≥0" means)?
Well, the term (x+1)² is always nonnegative, because it's a square. In fact it is
positive for all x≠1, only for x=1 is it zero.
So the entire lefthand side of the inequality is nonnegative when x is nonnegative, i.e. for all x≥0, and when x=1. In interval notation, you could write the solution set as
{1}∪[0, ∞).
Sep 25

Andre W.
Comments