How do you find the zeros of the polynomial function with equation # f(x) = -3(x+1/2)(x-4)^3#?

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Answer 1 · 2016-08-11T05:48:06

The zeors of #f(x)# in this case are #x = -1/2 or +4#

#f(x) = -3(x+1/2)(x-4)^3 #

The zeros of #f(x)# occur where #x# satisfies #f(x)=0#

Since #f(x)# is already factorised in this example, #f(x) =0# when

either:

#(x+1/2) = 0 -> x=-1/2#

or:

#(x-4)=0 -> x=+4#

This may be easier to visualise from the graph of #f(x)# below:

enter image source here

For interest: #f(x)# reaches a maximum value at #x=5/8#