How do you find all zeros of the function #f(x)=x^3(x-2)^2#?

1 Answer
Feb 26, 2016

Answer:

#x=0,2#

Explanation:

To find all the zeros of the function, set each factor to #0# and solve for #x#.

In your case:

#x^3=0#
#x=root(3)(0)#
#color(green)(x=0)#

#x-2=0#
#color(green)(x=2)#

You can see this holds true graphically as well:

graph{x^3(x-2)^2 [-5, 5, -2.5, 2.5]}

#:.#, the zeros of the function are #x=0# and #x=2#.