
Figure 1: Graph of f(x)=(x1)(x1)(x+2) 
 
A multiple root of a
polynomial
is a root that occurs more than once.^{[1]}
Take the polynomial in figure 1,
. The factor
occurs twice, so it is a
multiple root. Since it occurs twice, it is also called a
double root. The graph of polynomials with a
double root just touches the xaxis at the root then changes direction.
Figure 2 shows the graph of the polynomial
.
In this polynomial, the term
occurs 3 times. It has a
multiplicity
of 3. It is also called a
triple root. Note that the graph of the
polynomial crosses the xaxis at the triple root.


Figure 2: Graph of f(x)=(x1)(x1)(x1)(x+2) 
