If a polynomial function f (x) has roots 0, 4, and 3 + square root 11, what must also be a root of f (x) ?

3-√11

This function is evidently a quartic - a function with 4 roots. The last root has been found using the quadratic formula however, the answer always comes in pairs because the formula is

{b+√ (b^2 - 4ac) }/2a and {b-√ (b^2 - 4ac) }/2a. Therefore the other root must be 3-√11