Solving a cubic non-linear inequality

[aew782]

I just can't figure this out one question from my review test. I don't know hot to express it graphically or algebraically.

 

[SteamKing]

I don't see any inequality.

As far as expressing the equation graphically, you just plot it.

 

[symbolipoint]

I just can't figure this out one question from my review test. I don't know hot to express it graphically or algebraically.

Try to decompose the cubic expression to find the zeros, meaning find if possible its linear and any quadratic factors (if quadratic factor cannot be factored further). It may have as many as three zeros, but not more. The function (now being equal to zero) is in possibly four intervals. You don't show us the direction of your inequality but you say you want to analyze the inequality; but anyway, you check the quality of the value of the "inequality" for each interval of the x-axis and determine if the x value is true for the inequality or false.

EDIT: harder than I thought. +1 is not a root and -1 is not a root. Rational Root theorem will not work.

 

[micromass]

See http://en.wikipedia.org/wiki/Cubic_function#Cardano.27s_method