Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2018 / Paper 1 / 2

Move the constant term to the left and factor the cubic polynomial:Setting each factor to zero gives all three polynomial roots:

The quadratic formula gives the two polynomial roots $(-3\pm \sqrt{5})/2$. Its leading coefficient is positive, so the quadratic polynomial is strictly negative between them. Therefore