Question

Find the cubic function with given roots. See next comment.

Answer 1

\[1, 1 + \sqrt{2}, 1 - \sqrt{2}\]

Answer 2

Hint:
There can be many cubic functions with the given roots, in the form
f(x)=a(x-x1)(x-x2)(x-x3)
where x1,x2,x3 are the roots of f(x), and a is a non-zero constant.