If the equation x² - px - q = 0 has roots u and v, where p and q are non-zero constants, then consider the following statements

I. qx² + px - 1 = 0 has roots \(\frac{1}{u}\) and \(\frac{1}{v}\).

II. (x - p) (x + q) = 0 has roots u + v and uv.

III. x² + p²x + q² = 0 has roots u² and v².

Which of the above statement(s) is/are correct?