Polynomial Roots

number of roots

c

n

3

roots of polynomial:

c

1

1

c

2

2

c

3

3

c

4

0

c

5

0

c

6

0

c

7

0

c

8

0

c

9

0

The graph of a polynomial with roots

c

1

,

c

2

,

c

3

,…

meets the

x

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.