Algebra
# Quadratic Discriminant

Find the number of positive real roots of the equation $x^{4}-4x-1=0.$

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

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

Find the number of real roots of the polynomial $3x^{5} -25x^{3} +60x$.