
Figure 1: Graph of
f(x) = (x  1)(x 
1)(x + 2) 
 
A multiple root of a
polynomial
is a root that occurs more than once.^{[2]}
Take the polynomial in figure 1,
(x  1)(x  1)(x + 2)
The factor (x  1) occurs twice, so it is a
multiple root. Since it occurs only 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
(x  1)(x  1)(x  1)(x + 2).
In this polynomial, the term (x  1)
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) = (x  1)(x 
1)(x  1)(x + 2) 
