How do you write a polynomial function in standard form with Zero: 0, multiplicity 2?

1 Answer
May 11, 2016

Answer:

#f(x)=x^2# is one function that meets the specified requirements.

Explanation:

If #f(x)# has a multiplicity of 2 then for every value in the range for #f(x)# there should be 2 solutions.

Note that this would be true for #f(x)=x^2# since if #a# is a value in the range for #f(x)# then there are 2 solutions for #x#, namely #x=-sqrt(a)# and #x=+sqrt(a)#

Note that if #f(x)# has a zero at #x=0#
then #f(0)=0#
and again this will be true for #f(x)=x^2#

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

#f(x)=x^2# is not the only possible function meeting the requirements,
in fact
#color(white)("XXX")f(x)=k*x^2# for any integer value #k# will also work.