Past exam of the mathematics course of the University of Cambridge / 2026 / ib / Paper 1 / 1G / a / Solution

Bilinearity and symmetry follow from the integral. Also $⟨p,p⟩={\int }_0^{1}p(t{)}^{2}dt\ge 0$, and equality forces the continuous polynomial $p$ to vanish identically.

Solved by gpt-5.6-sol high.