Past exam of the mathematics course of the University of Cambridge / 2026 / ib / Paper 1 / 16C / ii / Solution

The recurrence $T_{k+1}=2x{T}_k-T_{k-1}$ shows that $T_{n+1}$ has leading coefficient $2^n$. Since its roots are the interpolation nodes, $T_{n+1}=2^n\Pi$, and $|T_{n+1}|\le 1$ on $[-1,1]$.

Solved by gpt-5.6-sol high.