$$\{p ∈ P_2 \mid p(1)+p(3)=0\}$$
I have been trying to understand how to go about solving this but I do not understand the expression $p(1)+p(3)=0$. If this constraint is instead $p(1)=0$ and $p(3)=0$ I could solve it but I do not know what the difference is.
If someone could please explain. Thank you.
If $q(x)=ax^2+bx+c \in P_2$, then $q(1)=a+b+c$ and $q(3)=9a+3b+c$. Hence:
$$ q \in \{p \in P_2 |p(1)+p(3)=0\} \iff 5a+2b+c=0.$$
Can you proceed ?