How do you find all the zeros of #f(x) = x^2 - 12x + 20# with its multiplicities?

1 Answer
Mar 27, 2016

Answer:

#f(x)=0# when #x=10# or #x=2# each with multiplicity #1#

Explanation:

Here are a couple of methods:

Completing the square

#f(x) = x^2-12x+20#

#=(x-6)^2-36+20#

#=(x-6)^2-16#

#=(x-6)^2-4^2#

#=((x-6)-4)((x-6)+4)#

#=(x-10)(x-2)#

So #f(x)=0# when #x=10# or #x=2# with multiplicity #1#

#color(white)()#
Product and sum

Note that #10*2 = 20# and #10+2 = 12#

So:

#f(x) = x^2-12+20 = x^2-(10+2)x+(10*2) = (x-10)(x-2)#

So #f(x)=0# when #x=10# or #x=2# with multiplicity #1#