What are the zeros of the polynomial function# f(x) = x^3 – x^2 - 12x#?

1 Answer
Mar 15, 2016

Answer:

The zeros occur at #x in {0,4,-3}#

Explanation:

Given
#color(white)("XXX")f(x)=x^3-x^2-12x#

Factoring:
#color(white)("XXX")f(x)=x(x^2-x-12)#

#color(white)("XXXXX")=x(x-4)(x+3)#

The zeroes of a function are the values of #x# for which the function's value is zero.

#color(white)("XXX")f(x)=x(x-4)(x+3)=0#
implies
#color(white)("XXX")#either
#color(white)("XXXXX")x=0#
#color(white)("XXX")#or
#color(white)("XXXXX")(x-4)=0 rarr x=4#
#color(white)("XXX")#or
#color(white)("XXXXX")(x+3)=0 rarr x=-3#