Given a sum of orthogonal polynomials $f(x)=\sum_{k=0}^{d}a_k P_k(x)=0$ where $x>0$, can I say that $a_k=0 \ \forall k$?

Question

I think I can use the recursive argument that because the leading coefficient of the highest order polynomial $P_k$ is unequal to zero the corresponding $a_{d}=0$.