How do you find all the zeros of #f(x) = x^2 - 4x - 60# with its multiplicities?

1 Answer
Apr 6, 2016

Answer:

#f(x)# has zeros at #x=6# and #x=-4# (there are only #2# zeros including multiplicity)

Explanation:

Factoring
#color(white)("XXX")f(x)=x^2-4x-60#

#color(white)("XXXXX")=(x+4)(x-6)#

When #f(x)=0#
either
#color(white)("XXX")(x+4)=0 rarr x=-4#
or
#color(white)("XXX")(x-6)=0 rarr x=+6#

Since #f(x)# is a quadratic (i.e. of degree #2#)
it has (including multiplicity and possible complex values) exactly #2# zeroes.