Subspace of polynomials, find basis

[MacroLand]

Trying to solve a question in linear algebra. P2 is a polynomial space with degree 2.

Is P(t): P'(1)=P(2) (P' is the derivative) a subspace of P2. What is the basis ?

It seems that it is a subspace with basis 1-t,2-t². Can anybody explain how this can be found?

 

[Dick]

An element of P2 is a polynomial P(x)=ax^2+bx+c. Put that into P'(1)=P(2) and figure out what condition a, b and c have to satisfy.