Inequality . . .

S

szcoup

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Aug 7, 2012
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Working on review assignments, and I've come across a problem that has tripped me up:

2x^3 + 5x^2 > 6x + 9
I did this:
2x^3 + 5x^2 -6x - 9 >0
I then grouped,
x^2(2x + 5) - 3(2x + 3) >0
this has me questioning how I am doing this, since usually the information in the ( ) are the same, not different. Have I gone wrong here? Thanks
 
No, I would not say that you went wrongly. I would say nice try, too bad elementary grouping didn't work out this time.

There are other ways to find roots of 3rd-degree polynomials.

For me, this paper-and-pencil situation screams for the Rational Roots Test and synthetic division.

Have you heard of either? :cool:


I'm guessing that your plan is to use the roots to divide the Real number line into intervals, followed by test values for x in those intervals.
 
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After 1 root is found, factor it out of the cubic using synthetic division. This leaves a quadratic and quadratic formula finds the remaining 2 roots if they exist.

Sometimes making a quick sketch of the graph will let you stumble upon one of the roots fairly quickly or at the very least narrow down the places to check with rational root test.
 
Just because he tried to do it by grouping doesn't mean the instructions said do by grouping. -_-
 
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