Final answer:
Heapsort operates in O(n log n) time complexity, not quadratic time; it is not considered slow relative to sorting algorithms that operate in quadratic time.
Step-by-step explanation:
False: Heapsort does not run in quadratic time; it operates in O(n log n) time complexity on average and in the worst case.
Heapsort is a comparison-based sorting algorithm that uses a binary heap data structure. It organizes the elements to be sorted into a heap, ensuring that the heap property is maintained throughout the sorting process. The complexity of building a heap is O(n), and the process of repeatedly removing the max element and restoring the heap property (heapify) takes O(log n) time for each of the n elements. This means that the overall average and worst-case time complexity of heapsort is O(n log n), not quadratic time, which is O(n^2). While heapsort is not as fast as other divide-and-conquer sorting algorithms like quicksort in practical situations due to its larger constant factors, it's still much faster than quadratic algorithms like bubble sort or insertion sort under most circumstances.
Furthermore, heapsort has the advantage of a guaranteed worst-case time complexity of O(n log n), unlike quicksort which can degrade to quadratic time complexity in the worst case if not implemented with randomization or pivot selection strategies.