Let Q = x² + bx + c. If the sum of the roots is equal to product of the roots of the equation Q = 0, then which of the following statements is/are correct? I. Q can be a perfect square. II. Q is positive for all real values of x.

For Q = x² + bx + c = 0, sum of roots = -b and product = c. Given -b = c, so b = -c. Then Q = x² - cx + c. Statement I: Q is a perfect square when discriminant = 0, i.e., c² - 4c = 0 giving c = 0 or c = 4. For c = 4, Q = x² - 4x + 4 = (x-2)², a perfect square. So I is correct. Statement II: Q is positive for all real x only when discriminant < 0, i.e., 0 < c < 4. This is not true for all valid c (e.g., c = 5 gives Q with real roots, so Q is negative somewhere). So II is not always correct.