3. Find the range of values of m if

has real and distinct roots.

This is the same as #2, but this time, since we want real and distinct roots, the discriminant has to be positive, or . So

a = 1

b = 1 - m

c = 1 - 2m

I want to find the zeros of the polynomial . Let's pretend for a moment that it equals 0 and solve for m:

Make a sign chart. Draw a number line and the critical points (the zeros we found earlier):

Code:

---------+-------------------+---------
-6.46 0.46

( and )

You have 3 intervals to test:

From each interval, pick a number inside it to test into the inequality , in order to determine the sign. The signs of the polynomial for each interval is as follows:

Code:

---------+-------------------+---------
pos -6.46 neg 0.46 pos

So the answer is .

01