SOLUTION: Im trying to find the quadratic inequality of 3x^2 + 9x <= 4 Can somebody please explain step by step how to find the answer. The two things I seem to be confused by the most is

Question 969636: Im trying to find the quadratic inequality of 3x^2 + 9x <= 4
Can somebody please explain step by step how to find the answer. The two things I seem to be confused by the most is the "3x^2" part because I'm used to problems that start with just "x^2" and the "<=". Any help would be highly appreciated.
Answer by josgarithmetic(39616) (Show Source): You can put this solution on YOUR website!
Put into general form, and either factor if possible, or use general solution for finding roots or quadratic expression.

Try search for factorability:
(3x 2)(x 2)------2x and 3x------not useful.
(3x 1)(x 4)-------1x and 12x-----no useful.
(3x 4)(x 1 )-----4x and 3x------no use.
The quadratic expression is not factorable with simple integers.

Check discriminant:

Roots are the critical values:
and

You can check the three intervals of the x-axis to determine where is the solution. Pick any single value in each of these intervals:
-

-

The exercise must be in the intermediate level because the quadratic part is not factorable and needs the general solution of finding roots for a quadratic expression for defining intervals. No way trying to avoid starting with "" or what "<=" means.
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