 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/ib/paper-1/1g/a/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

Bilinearity and symmetry follow from the integral. Also

⟨ p, p ⟩ = \int_{0}^{1} p (t)^{2} d t \geq 0

, and equality forces the continuous polynomial

p

to vanish identically.

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