1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Solving inequalities algebraically, when root is 0

  1. Mar 25, 2013 #1
    1. The problem statement, all variables and given/known data
    Solve each inequality without graphing the corresponding function.

    State the solution algebraically and graph on a number line:

    x/x2-9≤0

    so i factor out the denominator and get (x+3)(x-3) the root here is zero, but for some reason in the chart (for rational/reciprocal functions) they seem to treat the vertical asymptotes (x=-3, x=3) as root as well... so really instead of having 1 root, of 0, you now have what look like 3 roots, at x=0, x=-3, x=+3

    Now i've only learned how to solve inequalities algebraically this morning from this very helpful youtube video:


    http://www.youtube.com/watch?v=a9dzsIxcI-o&list=FLU9AMIFm9OGP9S3RGgO_hjw&index=1

    and according to this 'method' which i like VERY much....i keep getting the wrong answer/sum for the positives/negative intervals if the zero is equal to 0


    the book already shows me what the solution is i just dont know how to deal with these roots of 0 in situations like these, can anyone help?



    anything would be greatly appreciated, thanks :)
     
  2. jcsd
  3. Mar 25, 2013 #2
    for zero solution mark zero on the number line and proceed
     
  4. Mar 25, 2013 #3
    oh hey...i think your right...even if just move in the general direction it will tell me weather or not its positive or negative...

    and then i can multiply all the postives/negatives and determine weather the graph in that interval is above 0 or below 0




    thanks
     
  5. Mar 25, 2013 #4

    SammyS

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Gold Member

    You have written your algebraic expression incorrectly.

    x/x2-9 is technically equivalent to [itex]\displaystyle \ \frac{x}{x^2}-9\ [/itex] which is [itex]\displaystyle \ \frac{1}{x}-9\ .[/itex]

    You need to use parentheses and write x/(x2-9) which is [itex]\displaystyle \ \frac{x}{x^2-9}\ .[/itex]
    For a rational expression, the critical points are the roots of the numerator together with the roots of the denominator.

    This is because the sign of a rational expression will change if either the numerator or denominator changes sign.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Solving inequalities algebraically, when root is 0
  1. Solve this inequality (Replies: 2)

Loading...