Problem:
For which numbers
will the function
satisfy
for all
?
------------------------------------------------------------------------
Attempt: Correct up to here.
By using polynomial division I get the following result:
The trouble with this is that you are about to find that a = –d, so the denominator of the fraction in parentheses is zero.
By doing some hopefully correct algebra I get:
1.
So,
2.
So,
If
and
have opposite signs, their product is negative, and they can be any number.
If on the other hand, their signs are the same, their product is positive and:
-----------------------------------------------------------------------
Am I making this more complicated than it is?
How can I better express my results regarding
, and
?