Question 5900: Can someone please explain how to solve quadratic inequalitities using sign charts. I has me a little confused and I have about 30 problems to do. Here is an example of one.
solve (x-5)(x+2)>0 using a sign chart.
Thanks Caroline
Answer by longjonsilver(2297)   (Show Source):
You can put this solution on YOUR website! First, understand that the (x-5)(x+2) is a quadratic, which may (or may not) cross the x-axis. So, at some points, the curve may have a -ve y-value or a +ve y-value, and this will flip at the point(s) where the curve crosses the x-axis..the root(s) of the equation.
here is this equation... 
From the graph, you instantly see the answers for your "sign chart"...
below x=-2, the curve is +ve
Above x=+5, the curve is +ve
between these 2 values, the curve is -ve.
So...in a sign chart - the following numbers are gotten from the equation written in its factored form, since this tells you the roots (where the curve crosses the x-axis)
x<-2__x=-2__between___x=5___x>5
+_______0______-______0_____+
(ignore the __ symbols...they are there to give equal spacing. Also, between is just me explaining the region between x=-2 and x=5, as i cannot write it here :-( ).
Simply, put a value, say x=+10 into the equation (x-5)(x+2) --> get (10-5)(10+2) which is (+)(+)...+ and a + makes + (we are not interested in the numerical part..just the sign.
Another example: take x=-10... (x-5)(x+2) --> (-10-5)(-10+2) --> (-)(-) --> +
Is this OK? Basically, the "sign chart" is to get out of sketching (not plotting) the graph, but the best thing you can ever do in any question is draw a picture, so i would concentrate on doing the sketch.
Anyway, back to the question..if it said solve (x-5)(x+2)>0, then you would know it was te 2 regions x<-2 and x>+5. etc
jon.
|
|
|
