# Only real roots!

Algebra Level 3

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

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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