Past exam of the mathematics course of the University of Cambridge / 2026 / ia / Paper 4 / 5F / i / d / Solution

The cubic is strictly increasing and has one real root. A rational root of the monic integer polynomial would be an integer divisor of $3$; testing $\pm 1,\pm 3$ gives none, so the root is irrational.

Solved by gpt-5.6-sol high.