|Figure 1: Graph of f(x)=(x-1)(x-1)(x+2)||
A multiple root of a
is a root that occurs more than once. 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 x-axis at the root and changes direction.
Figure 2 shows the graph of the polynomial
In this polynomial, the term
occurs 3 times. It has a
of 3. It is also called a
triple root. Note that the graph of the polynomial crosses
the x-axis at the triple root.
|Figure 2: Graph of f(x)=(x-1)(x-1)(x-1)(x+2)|