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

1 Answer
Sep 12, 2016

Answer:

#x= 5#
#x=-4#

Explanation:

set the equation equal to 0 and solve for each part containing an #x#.
#2(x-5)(x+4)^2 = 0#

#(x-5)= 0#
#(x+4)^2=0# or #(x+4)(x+4)=0# so #x+4=0#

this is a valid approach because its multiplicative and a #0# in any part of the equation will result in #0#.

#x= 5#
#x=-4#

we then plug this into the equation to verify that it works and retain the ones that do. In this equation they both are valid.