We want to find an equation for the given solutions and the multiplicity of each solution.
The equation is:
First, assume that we have a given equation and we know that we have solutions {x₁, x₂, ..., xₙ}, each one with multiplicity {m₁, ..., mₙ}.
The equation, of a polynomial that meets these requirements, is given by:
Where A is the leading coefficient and can be any real number.
Now that we know that, here we have the solutions:
- x = 2 with multiplicity 2
- x = -1 with multiplicity 2
We don't have information about the leading coefficient, so we assume it is equal to 1.
Then the equation is:
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