Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2021 / Paper 1 / 2 / Solution

Find two numbers with sum $-1$ and product $-2$: they are $-2$ and $1$. Thus the quadratic polynomial factorizes asThe product is negative precisely when its two factors have opposite signs. This occurs between its two polynomial roots, soThe endpoints give zero and are excluded by the strict inequality.