College Algebra & Trigonometry, 2018a

2.3. SOLUTION OF POLYNOMIAL INEQUALITIES BY GRAPHING 97
10
y ≥ 0
5
A
B
y ≥ 0
−3 −2 −1 C 1
−5
The indicated roots of the function (A, B and C) are the x-values that make y
equal to zero. These points divide the graph between the regions where y is
greater than zero and the regions where y is less than zero. The solution to the
given inequlaity 2x 3 +8x 2 +5x − 3 ≥ 0 are A≤ x ≤B ORx ≥C.
When we find the values of A, B and C: A= −3,B≈−1.366 and C≈ 0.366, we can
complete the solution to the problem.
2x 3 +8x 2 +5x − 3 ≥ 0
−3 ≤ x ≤−1.366 OR x ≥ 0.366
Example
Solve the given inequality.
x 4 − 2x 3 − 5x 2 +8x +3≤ 0
First, we graph the function: