The Linux root partition is the partition that contains the root filesystem, which is the top-level directory of the filesystem hierarchy. The root filesystem contains the essential files and directories that are needed to boot the system, such as the kernel, the init system, the configuration files, the libraries, the binaries, and the device files. The root partition can be formatted with different filesystems, depending on the support of the kernel and the boot loader. Some of the common filesystems that can be used on Linux root partitions are:

ext3: This is the third extended filesystem, which is a journaling filesystem that provides metadata and data integrity, fast recovery, and backward compatibility with ext2. ext3 is widely supported by most Linux distributions and boot loaders, and it is considered stable and reliable. ext3 has been the default filesystem for many Linux distributions, such as Debian, Ubuntu, Fedora, and CentOS, until it was replaced by ext4.

XFS: This is a high-performance 64-bit journaling filesystem that supports large files and volumes, parallel I/O, extent-based allocation, and online defragmentation. XFS is designed for scalability and efficiency, and it is suitable for applications that handle large amounts of data, such as databases, video editing, and data warehousing. XFS is the default filesystem for Red Hat Enterprise Linux and SUSE Linux Enterprise Server, and it is also supported by other Linux distributions and boot loaders.

The other options are not valid filesystems for Linux root partitions, because:

NTFS: This is the New Technology File System, which is the default filesystem for Windows operating systems. NTFS supports features such as journaling, encryption, compression, and access control. NTFS is not natively supported by the Linux kernel, and it requires a third-party driver, such as ntfs-3g, to read and write to NTFS partitions. NTFS is not compatible with the Linux boot loader, and it cannot be used as the root filesystem for Linux.

VFAT: This is the Virtual File Allocation Table, which is an extension of the FAT32 filesystem that supports long file names. VFAT is a legacy filesystem that is mainly used for compatibility with older Windows and DOS systems. VFAT does not support features such as journaling, permissions, and symbolic links, and it has limitations on the file and volume size. VFAT is not suitable for the root filesystem for Linux, and it is not supported by the Linux boot loader.

swap: This is not a filesystem, but a special type of partition that is used to store the memory pages that are not currently in use by the system. swap is used to extend the physical memory of the system, and it can improve the performance and stability of the system. swap is not a mountable partition, and it cannot be used as the root filesystem for Linux.