# Only real roots!

Algebra Level 3

$$$$\displaystyle \prod_{k=1}^{999} (x^2-47x+k) = (x^2-47x+1)(x^2-47x+2)\dots(x^2-47x+999)$$$$

If the product of all real roots of the polynomial above can be expressed in the form $$n!$$, what is the value of $$n$$?

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