Advanced Functions - Case Method

There are 2 ways to solve a polynomial inequality using algebra. Interval Method, and Case Method.


The idea of the case method is to test all the possible results of the functions. Therefore take the function f(x) = x^2 + 9x + 20 , when factored is f(x) = (x+4)(x+5). So in this case each bracket can either be negative or positive. So the cases are:


Question: (x+4)(x+5) >= 0



Now each case must be tested by doing the following:





After repeating the above for the other 3 cases, it would be found that the solution is:


F(x) >= 0 when XE(-infinity, -5]U[-4, infinity)


*Note that when the number line is created for the cases where one is negative and the other the lines will not overlap (FOR THIS EXAMPLE). Therefore that means that those cases will not have a solution and the solution will only consist of the cases where there is an overlap.


Clearly the case method can be very time consuming where there are more than 2 factors, therefore for more complicated inequalities it is easier to use the interval method.



If you have any questions, leave them in the comments below.