Find the x-intercepts of f(x)=x(x+1)^3(x-3)^2 and determine the behavior at the intercepts.

Answer 1

The x-intercepts of f(x) = x(x+1)³(x-3)² are 0, -1, and 3.

Since 0 and -1 are real roots with odd multiplicity, the graph crosses the x-axis when x = 0 and when x = -1.

Since 3 is a real root of even multiplicity, the graph intersects the x-axis at x = 3, but the graph does not cross the x-axis when x = 3.