Let be a polynomial of degree at most 2. Find all that satisfying the given conditions.
 .
 .
 .
 .
Since is a polynomial of degree at most 2 we may write,
for constants.

We substitute,
Equating like powers of , we have,
Thus,
Or, since these are arbitrary constants we can relabel them,

Again, we substitute,
Again, equating like powers of ,
Hence,

Substituting,
Equating like powers of ,
Thus,

Substituting,
Equating like powers of ,
Hence,