[QUE/VS-02010]

PRO/VS-02010

Consider the set of all polynomials \(p(t)= a_0 +a_1 t + a_2 t^2\) for which

1. \(p(0)=0\)
2. \(2p(0)=p(1)\)
3. \(p(t)=p(1-t)\)
4. \(p(1) > 0\).

Give the dimensions of the vector spaces wherever appropriate and give a possible basis?