How do you find all the zeros of #f(x) = 9x^3 - 45x^2 + 36x#?

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Answer 1 · 2016-04-09T10:28:44

#x = 0, 1, 4#

Factorise #f(x)# by taking out #9x#, the greatest common factor, and going from there,

#f(x) = 9x^3 - 45x^2 + 36x#
# = 9x(x^2 - 5x + 4)#
# = 9x(x - 4)(x - 1)#

One of these three parts has to equal #0# for the whole thing to be #0#, so you'll end up with three answers.

#9x = 0#
#x = 0/9 = 0#

#x - 4 = 0#
#x = 4#

#x - 1 = 0#
#x = 1#

and you've got your answers.