An AVL tree is a balanced binary search tree where the height of the two child subtrees differ by at most one, otherwise known as height-balanced[?]. Look-up, insertion and deletion are all O(log(n)) in both the average and worst cases. Additions and deletions may require the tree to be rebalanced by one or more tree rotations. The AVL tree is named after its inventors, Adelson-Velskii[?] and Landis[?] (1962).
... roots numerically, the usual form of the quadratic formula is not ideal. See Loss of significance for details.
Derivation
The quadratic formula is derived by ...