We address the complex problem of reliably segmenting root structure from soil in X-ray Computed Tomography (CT) images. We utilise a deep learning approach, and propose a state-of-the-art multi-resolution architecture based on encoderdecoders. While previous work in encoder-decoders implies the use of multiple resolutions simply by downsampling and upsampling images, we make this process explicit, with branches of the network tasked separately with obtaining local high-resolution segmentation, and wider low-resolution contextual information. The complete network is a memory efficient implementation that is still able to resolve small root detail in large volumetric images. We compare against a number of different encoder-decoder based architectures from the literature, as well as a popular existing image analysis tool designed for root CT segmentation. We show qualitatively and quantitatively that a multi-resolution approach offers substantial accuracy improvements over a both a small receptive field size in a deep network, or a larger receptive field in a shallower network. We then further improve performance using an incremental learning approach, in which failures in the original network are used to generate harder negative training examples. Our proposed method requires no user interaction, is fully automatic, and identifies large and fine root material throughout the whole volume.