Only real roots!

Level pending

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

If the product of all real roots of the polynomial above can be expressed as \(n!\), what is the value of \(n\)?

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