College Algebra & Trigonometry, 2018a

2.3. SOLUTION OF POLYNOMIAL INEQUALITIES BY GRAPHING 99
5
−2 −1 1 2
y ≤ 0 y ≤ 0
−5
So, the solution to the original inequality is:
x 4 − 2x 3 − 5x 2 +8x +3≤ 0
−2.034 ≤ x ≤−0.320 OR 1.806 ≤ x ≤ 2.549
In the next example we’ll be looking to identify both the intervals where y is
greater than zero, and the intervals where y is less than zero.
Example
Determine the interval(s) for which x 3 +5x 2 +5x +1≥ 0
Determine the interval(s) for which x 3 +5x 2 +5x +1< 0
Once again, we’ll start by graphing the function to find the roots: