To find the zeros, or x intercepts, set the equation equal to zero.
f(x)=0 at the x intercepts.
2(x−5)(x+4)2=0
x−5=0 and x+4=0
x=5 and x=−4
The zero at x=5 has a multiplicity of one, because the exponent on the factor (x−5) is one. A zero with odd multiplicity indicates the graph crosses the x-axis at that point.
The zero at x=−4 has a multiplicity of two, because the exponent on the factor (x−4)2 is two. A zero with even multiplicity indicates the graph just touches the x axis and then turns back in the same direction, i.e. the graph does not cross the x-axis.
