A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

does anyone know the way to solve this Polynomial Inequality? x^2(3+x)(x+4)/((x+5)(x-1))>=0 I would like to know how to determine the negative and positive factors of the equation.

  • This Question is Closed
  1. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    The way I always learned it was to look for critical points (I think there is a better word for this). Those would be x=0,-3,-4,-5,1 (it comes from equation given). These would be different "critical points" on a number line. Then you can test the points in between these critical points.Then we get that: x<-5, -4<=x<=-3, x=0, x>1 Note: the reason why some are < while others are <= is because if you were to examine the equation you would realize that it cannot be -5 since that would mean division by zero. On the other hand it could be -4, thus it would have that equation factor as well.

  2. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Thank you for the reply. I guess I just do not really understand these types of problems, especially the part about testing the points in between the critical points. I do appreciate your response. Perhaps I can try to find a video to explain it in more graphical terms.

  3. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    It's because rational functions (rational functions are functions in which the numerator and denominator are both polynomials) are continuous whenever the denominator isn't 0. They are continuous because polynomials are continuous. Continuous functions have something called the "Intermediate Value Property." Basically, suppose that at x = a, the function is negative. Then later at x = b, the function is positive. If the function is continuous, then at some point x = c between a and b, the function must have been 0. That’s why looking for zeros and points of discontinuities is important. It tells you places where the function can change signs from positive to negative. Looking for zeros and points of discontinuities is called looking for critical points. In your function, the critical points are x = -5, -4, -3, 0, and 1. So that means if your function is positive for x = 100000, it follows that the function is positive on the interval 1 < x < infinity. That’s because there are no critical points greater than x = 1. So if f(x) is positive for some random value x where x > 1, then f(x) must be positive throughout the entire interval past x > 1. If f(x) is positive for x = -1000000, then x is positive throughout the entire interval -infinity < x < -5 for the same reason. If f(x) is positive for x = -1, then f(x) is positive throughout the entire interval -3 < x < 0, since those are the critical points that surround x = -1. We know that f(x) can’t become negative somewhere in that interval since if it became negative, there should be some other critical point in the interval -3 < x < 0, but there are none. Apply that reasoning to test whether f(x) is non-negative for the remaining intervals.

  4. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.