How do you find all the zeros of #F(x) = -4 (x+7)^3 (x-7)^2# with all its multiplicities?

1 Answer
Oct 10, 2016

Answer:

#F(x)# has zeros at #(-7)# with multiplicity of #3# and at #(+7# with a multiplicity of #2#

Explanation:

#F(x)=-4(x+7)^3(x-7)#^2#

A term of #(x+7)# implies a zero at #x=-7#
A term of #(x+7)# implies a zero at #(x=+7#

#F(x)=-4 * underbrace((x+7)(x+7)(x+7))_"multiplicity of 3" * underbrace((x-7)(x-7))_"multiplicity of 2"#