# Polynomial Roots

This worksheet illustrates how the roots of a polynomial
affect its behavior. Below is a plot of the polynomial

$$p\left(x\right)=\left(x-a\right)\left(x-b\right){x}^{n-2},$$
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.

## Questions

- Change the value of \(b\) to \(1.0\). What happens to the graph of the polynomial?
- 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?
- 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?
- 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?