How do you find all the zeros of #f(x) = 2(x-5)(x+4)^2 #?

1 Answer
Sep 18, 2016

Answer:

The zeros (where# f(x)=0#) are located at #x=5# and #x=-4#.

Explanation:

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.