Polynomial Roots

The graph of a polynomial with roots meets the axis at those roots. At a simple root, the curve crosses the axis at an angle. At a multiple root, the axis is tangent to the curve. If the multiplicity is odd (and greater than one), the curve has a flat inflection point at the root. If the multiplicity is even, the curve has a minimum or a maximum at the root, depending on the sign of the leading term and the position of the other roots.