It doesn’t work because you didn’t attach the ScrollPane to the JFrame.
Also, you don’t need 2 JScrollPanes:
JFrame frame = new JFrame ("Test");
JTextArea textArea = new JTextArea ("Test");
JScrollPane scroll = new JScrollPane (textArea,
JScrollPane.VERTICAL_SCROLLBAR_ALWAYS, JScrollPane.HORIZONTAL_SCROLLBAR_ALWAYS);
frame.add(scroll);
frame.setVisible (true);