Which of the following is an example of an insect pest that affects roots?

Root-feeding beetles are a prime example of an insect pest that affects roots. These beetles, as larvae, specifically target the root systems of plants, feeding on them and potentially causing significant damage. This feeding can disrupt water and nutrient uptake, ultimately leading to poor plant health and reduced crop yields.

In contrast, other options like leafhoppers primarily feed on the sap of stems and leaves, while spider mites are known for infesting leaves and causing damage by sucking out plant fluids. Cutworms, although they can be problematic for young plants, typically feed on the stems near the soil surface rather than directly on the roots. Therefore, root-feeding beetles stand out as the correct choice for an insect pest that specifically targets and damages plant roots.