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

Algebra ->  Inequalities -> 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      Log On


   

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) About Me  (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.

3x%5E2%2B9x-4%3C=0

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:
%289%5E2%29-4%2A3%2A%28-4%29
81%2B16
97

Roots are the critical values:
%28-9-+sqrt%2897%29%29%2F6 and %28-9%2B+sqrt%2897%29%29%2F6

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:
-
x%3C=%28-9-sqrt%2897%29%29%2F6
-
%28-9-sqrt%2897%29%29%2F6%3C=x%3C=%28-9%2Bsqrt%2897%29%29%2F6
-
%28-9%2Bsqrt%2897%29%29%2F6%3C=x
-

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 "x%5E2" or what "<=" means.