Consider the following statements: I. √x + x + 1 = 0 has two irrational roots. II. 5√x - x - 4 = 0 has two rational roots. Which of the statements given above is/are correct?

I. √x + x + 1 = 0: Let y = √x ≥ 0, then y² + y + 1 = 0, discriminant = 1 - 4 = -3 < 0, no real roots. So statement I is false. II. 5√x - x - 4 = 0: Let y = √x, then -y² + 5y - 4 = 0, y² - 5y + 4 = 0, (y-1)(y-4) = 0, y = 1 or 4, so x = 1 or 16, both rational. Statement II is correct.