I have been informed that on March 7th from 6:00am to 6:00pm Central Time Lamar University will be doing some maintenance to replace a faulty UPS component and to do this they will be completely powering down their data center.
Unfortunately, this means that the site will be down during this time. I apologize for any inconvenience this might cause.
Paul
February 18, 2026
Section 2.12 : Polynomial Inequalities
5. Solve the following inequality.
\[{y^2} - 2y + 1 \le 0\]Show All Steps Hide All Steps
Start SolutionThe first thing we need to do is get a zero on one side of the inequality (which is already done for this problem) and then, if possible, factor the polynomial.
\[{\left( {y - 1} \right)^2} \le 0\]Despite the fact that this is an inequality we first need to know where the polynomial is zero. From the factored from we can quickly see that the polynomial will be zero at,
\[y = 1\]This problem works a little differently than the others in this section. Because the polynomial is a perfect square we know that it can never be negative! It is only possible for it to be zero or positive.
We are being asked to determine where the polynomial is negative or zero. As noted however it isn’t possible for it to be negative. Therefore the only solution we can get for this inequality is where it is zero and we found that in the previous step.
The answer is then,
\[\require{bbox} \bbox[2pt,border:1px solid black]{{y = 1}}\]In this case the answer is a single number and not an inequality. This happens on occasion and we shouldn’t worry about these kinds of “unusual” answers.