Question

How do you find the polynomial function with roots 2, `3+- sqrt2`?

Answer 1

Start from the factored form to find the desired polynomial to be
`f(x)=x^3-8x^2+19x -14`

Explanation:

Creating a polynomial function with specific roots is as easy as can be. Just set it up as a product of binomials `(x-"root")` which evaluate to `0` at the desired root. For example, in this case, we would use

`f(x) = (x-2)(x-(3+sqrt(2)))(x-(3-sqrt(2)))`

`=x^3-8x^2+19x -14`

Because we start from the fully factored form, it is clear that the roots are as desired.