The number of points, where the curve y=x5−20x3+50x+2 crosses the x-axis, is _____.

The curve y = x^5 - 20x^3 + 50x + 2 crosses the x-axis where y = 0.

So, we need to solve the equation x^5 - 20x^3 + 50x + 2 = 0 for x.

This is a quintic equation and can be quite complex to solve. However, we can try to factor it or use numerical methods to find the roots.

Unfortunately, this equation doesn't factor nicely, so we'll have to use numerical methods like the Newton-Raphson method, bisection method, or using software tools like Wolfram Alpha to find the roots.

The number of roots of the equation will be the number of points where the curve crosses the x-axis. Each root represents a point where y = 0, i.e., where the curve crosses the x-axis.

Please note that without specific numerical methods or software, it's not possible to find the exact roots of this equation.