Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 160 / 1 / c / ii / Solution

The nonzero coefficients and part a(ii) give unique elements $h\in C(t)$ and $h^{\ast }\in C(t^{\ast })$ such thatPart i gives $h=h^{\ast }=:k$, so $k\in C(t)\cap C(t^{\ast })$. Both coefficients are then $\mathrm{sgn}(k)$ and hence are equal.