Joe Root his first golden duck in his ODI career. The 5th ODI was better for Root as he scored a quick 21 before being bowled and also took the wicket of George Bailey. England lost the series 2–1 and Root finished the series with 36 runs and 1 wicket. Root was selected for the 2013-14 Ashes series. He was selected at number 6 for the first Test as Michael Carberry was given the opening batsman role alongside Alastair Cook. Root only managed 2 runs from 7 balls in the first innings before being caught off a Mitchell Johnson delivery. In the
Root system with no overt connection to Lie theory (such as singularity theory). Finally, root systems are important for their own sake, as in spectral graph theory. As a first example, consider the six vectors in 2-dimensional Euclidean space, R, as shown in the image at the right; call them roots. These vectors span the whole space. If you consider the line perpendicular to any root, say β, then the reflection of R in that line sends any other root, say α, to another root. Moreover, the root to which it is sent equals α + nβ, where n is an integer