Polynomial Roots

This worksheet illustrates how the roots of a polynomial affect its behavior. Below is a plot of the polynomial
$px = x-a x-b xn-2,$ where $n$ is the degree of the polynomial and $a$ and $b$ are two real roots you can control with the sliders. Note that when the degree $n$ is greater than two then zero is always a root of the polynomial.

Value of root a:
Value of root b:
Degree of polynomial:

Questions

1. Change the value of $$b$$ to $$1.0$$. What happens to the graph of the polynomial?
2. Change the degree of the polynomial to 3. What happens to the graph of the polynomial? If you have had Calculus, how can you explain this in terms of the derivative?
3. Now make $$a = b = 1$$. What happens to the graph of the polynomial? If you have had Calculus, how can you explain this in terms of the derivative?
4. Change the degree of the polynomial to 4. What happens to the graph of the polynomial? If you have had Calculus, how can you explain this in terms of the derivative?