How do you find the zeros of the polynomial function #f(x)=x^3-13x^2+40x#?

1 Answer
Feb 13, 2016

Answer:

Zeros of the polynomial function are #0#, #5# and #8#.

Explanation:

To find the zeros of the polynomial function #f(x)=x^3−13x^2+40x#, We factorize it.

It is obvious that #x# is a factor and hence the polynomial function can be written as #f(x)=x(x^2−13x+40)#.

It is observed that #8# and #5# are two factors of #40# whose sum is #13#and hence #x^2−13x+40#, can be factorized as follows

#x^2−13x+40# = #x^2−5x-8x+40# = #x(x-5)−8(x-5)# =#(x-8)(x-5)#

And hence factors of the polynomial function #f(x)=x^3−13x^2+40x# are #x(x-8)(x-5)#

Hence zeros of the polynomial function are #0#, #5# and #8#.