solving quadratic, rational inequalities

jhawk555

New member
Joined
Sep 26, 2006
Messages
34
I think I am completely lost. This last lesson we did and I just can't seem to grasp what to do.

Can someone explain this or am I a lost cause?

1) -x^2 + 4x + 5 >= 0

I am not sure where to begin to solve to graph this other than -(x+5)(x+1)

I guess I can use the test point method, but I do not fully understand that.

Rational inequality example:

2) (x^2 - 5x + 6) / (2x - 7) <= 0

If anyone can shed some light on the subject, I would greatly appreciated.
 
1) Find the zeroes of the quadratic. These divide the number line into intervals. The "test-point method" says to pick a point from within each interval. For any given interval, plug that interval's test point (the x-value you've chosen from within that interval) into the quadratic. The numerical answer isn't as important as the sign. In this case, the solution is the interval(s) for which the test point returns a positive ("greater than zero") value.

2) Find the zeroes and undefined points of the rational. These divide the number line into intervals....

Eliz.
 
Top