Greetings,
is a given function.
We are looking for all values of a such that at least one of the solutions of the function is within the interval [-1;1].
So, I've come up with this:
to find all relevent a values for exactly when one x is within [-1;1], we need this:
-1 <= x <= 0, which happens when f(-1)f(1) <= 0. (1)
To find all relevent values of a for when we need both solutions to be within [-1;1], we need:
D>=0 (2)
af(1)>=0 (3)
-1<= -b/2a <= 1 (4)
and we put it all from 1 to 4 in a system.
For the solution of (1), I have:
a is from (-1-sqrt5) / 2 to -1 U from (-1+sqrt5) / 2 to 1
(Sorry, I couldn't get Latex to work.. )
For (2), I believe all values of a do the job..
For (3):
a (-infinity;(-1-sqrt5)/2] U [1;+infinity]...
and finally for (4):
[-1-sqrt3;-1+sqrt3]
So, when we combine all of this, eventually, I am left with:
a [-1; (-1-sqrt5)/2]... which is not correct.
The true thing is supposed to be:
[(-1-sqrt5)/2; 1]
Thank you..
and sorry again for the lame writing...