I think you want to create a navigation controller that you will present modally; the following will do:
SettingsViewController* settingsViewController = [[SettingsViewController alloc] initWithStyle:UITableViewStyleGrouped];
UINavigationController *navigationController = [[UINavigationController alloc] init];
[navigationController pushViewController:settingsViewController animated:YES];
[self presentViewController: navigationController animated: YES completion:nil];
where self
here is the view controller you want to trigger the modal view controller from.
since you present modally the navigation controller you can dismiss it within the code source of your settingsViewController by accessing its navigation controller:
[self.navigationController dismissViewControllerAnimated:YES completion: nil];
To answer your question setting the rootViewController is not the correct way. Present the new vc modally through the presentViewController
method.