Why is the only way for ax^2+bx+c=0 is if a=b=c=0?

Question

anonymous · Answer

it isn't

anonymous · Answer

ex: x^2-4x=0 a=1 b=2 c=0 (solution x=0 or x=4)

anonymous · Answer

b=-4 changed problem halfway through and did not change

anonymous · Answer

http://tutorial.math.lamar.edu/Classes/DE/PowerSeries.aspx bottom of page what does he mean then?

anonymous · Answer

i think the question should be asked like this:
Why is the only way for ax^2+bx+c to be 0 FOR ALL X if and only if a = b = c = 0.  Thats a true statement.

anonymous · Answer

oh i guess i didnt really say why did I.  its because x^2, x, and 1 are Linearly independent.  There is no multiple of 1 that will equal x, no multiple of x that will equal x^2, and no multiple of x^2 that will equal one.  By multiple, i mean by a scalar, or constant.

anonymous · Answer

It isn't necessary.

anonymous · Answer

We don't know if you are considering the vector space of polynomials or the equation.
If you are talking about the vector space then x is only a placeholder.

anonymous · Answer

I did not read carefully, it says FOR ALL X.