write a polynomial function of least degree with roots of 3 and 2-square root of 11

Answer 1

The answer to your question as you wrote it is (x-3)(x-2+sqrt(11)).

However, that is NOT the answer you will be expected to give.

The quadratic polynomial above does not have rational coefficients...but your question did not state that the polynomial must have rational coefficients!!!!!!!

The cubic polynomial with rational coefficients is (x-3)(x-2+sqrt(11))(x+2-sqrt(11))