critical values (where the left side equals 0) are and
solution set is
for further info, go to the link ...
Pauls Online Notes : Algebra - Polynomial Inequalities
We are doing a review of algebra 2 and I really need some help. I have a new teacher and I never learned it the way he taught us. He doesn't let us use calculators. So I was wondering if some of you could please help me with some equations! Solve the following polynomial inequalities.
1. (x+2)^2<25
2. 5z^2+26z+3<-2
3. X^4(x-3)<0
4. -2x^2-4x+2x^3 <0
5. 13x+4+5x^2>-2
If anyone could help me with these it would be great. And yes I have tried and been sitting here for an hour stuck on them so don't think I didn't even try. Thank you!
critical values (where the left side equals 0) are and
solution set is
for further info, go to the link ...
Pauls Online Notes : Algebra - Polynomial Inequalities
Isolate the squares, take the negative and positive square roots, and deal with the inequalities accordingly.
Here are a couple examples to get you started:
(1.)
(assuming x is real)
You sure you wrote #2 down correctly? It's gonna get awfully messy when you complete the square.
(3.)
because x^4 has to be nonnegative
For (2), write the inequality as . You can use the quadratic formula to find the roots of the equation, [tex]5x^2+ 26x+ 5= 0, a and b, and then factor as 5(x- a)(x- b)< 0. Of course, such a product will be negative if and only x- a and x- b have opposite signs. And that means x is larger than one of a and b and less than the other.
(4), can be factored as . And it is easy to factor . The product of three factors, (x- a)(x- b)(x- c) is negative if all three factors are negative or if two are positive and one negative.
(5), or , can be solved by using the quadratic formula to solve the equation for the roots a and b. And then the problem can be written as . That will be true if and only if x-a and x- b have the same sign- in other word if x is larger than both a and b or x is less than both a and b.