If f x = ∏ k = 1 999 x 2 - 47 x + k , then product of all real roots of f x = 0 is

Step-by-step solution

Consider x 2 - 47 x + k = 0 For real roots, 47 2 - 4 k ≥ 0 ⇒ k ≤ 552 ∴ k = 1, 2, 3 … . , 552 Product of real roots = 1 × 2 × 3 × 4 × … . . × 552 = 552 !