Question

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

Answer 1

`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`

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`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.