Hi In my calculus class today, we had a lesson on solving polynomial inequalities. However, after my classmates and I got the answers to the homework wrong and I checked the internet, I suspect my teacher taught us wrong. Before I do anything about it though, I want to check for certain whether or not the method he gave us is wrong.
He told us to factor the polynomial, then treat each one as a separate linear function, and just bring it over across the sign (obviously flipping it if you multiply or divide by a negative).
For example, here's what he showed us to do for this question:
-x^2 + 4x - 4 > 0
-(x-2)^2 > 0
(x-2)^2 < 0
x-2 < 0
Two identical solutions: x < 2
However, I found the correct answer on the internet and in the text to be x = 2. This is just one of many where the answer I got using his method was wrong. Is what he did correct, or should it be done as these sites say:
Solving Polynomial Inequalities
Solving Polynomial Inequalities Analytically
Thanks so much to anyone who takes the time to read this and help
EDIT: It should read greater than or equal to.
as Krizalid pointed out, you would end up with |x - 2|<0 and there is no solution to that equation, since |x - 2| >= 0 for all x
if the original question was really -x^2 + 4x - 4 >= 0 then the solution is x = 2 as your text says as the inequality |x - 2| =< 0 has x = 2 as the only solution