Hi.
I didn't have time to read all the topic. So excuse me if what I'm saying has already been told.
Please take time to read the following paragraph taken from Wikipedia:
Please pay attention to the difference between "undefined" and "indeterminate".
And about the following:
I remember someone answering that, equating coefficients is not possible for X=0 . Well that is not true at all.
The thing is that, no division happens at all.
Let me first give you the correct form of the question:
The following equation is true for all values of X . Find d,e and f . (values of a ,b and c are given on the question)
ax2 + bx + c = fx2 + gx + h
So this is what happens:
(a-f)x2 + (b-g)x + (c-h) = 0
Since the above equation is true for ALL values of X, the only logical answer would be: a=f b=g c=h
You could solve the equation for three values of X. let's say 1 and 2 and 3
1: (a-f) + (b-g) + (c-h) = 0
2: (a-f)*4 + (b-g)*2 + (c-h) = 0
3: (a-f)*9 + (b-g)*3 + (c-h) = 0
It is easy to solve afterwards.
You could also use Proof by contradiction.
Link to full wikipedia article: Division By Zero