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Polynomial Roots

​
number of roots
c
n
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.
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