Final answer:
The statement is false; in a B+ tree, duplicate entries of search keys are not allowed in any non-leaf nodes, including the root node. Non-leaf nodes only contain unique keys that act as an index to guide searches towards leaf nodes, which can contain duplicate search keys.
Step-by-step explanation:
The statement that among all the non-leaf nodes of a B+ tree index, duplicate entries of search keys are allowed in the root node is false. In a B+ tree, which is a type of self-balancing tree data structure that maintains sorted data in a way that allows for efficient insertion, deletion, and lookup operations, duplicate entries of search keys are not allowed in any non-leaf nodes, including the root. Each key in a non-leaf node of a B+ tree appears only once and serves as a guide to direct the search process towards the appropriate subtree that may contain the actual record or records in the leaf nodes.
The role of the root and every other non-leaf node is to act as part of the index to guide the search. The leaf nodes of a B+ tree contain all the actual records, and these records can be accessed by traversing the tree from the root down to the leaf level. It's within these leaf nodes that you may find duplicates of the search keys in a B+ tree, particularly in the context of storing multiple records with the same search key value.