What is the lowest possible degree of a polynomial with the following solutions? −4, 2+4i, and 6−7√

Question

What is the lowest possible degree of a polynomial with the following solutions? −4, 2+4i, and 6−7√

Answer 1

A polynomial with 3 solutions must be at least order 3. Keep in mind that some solutions may be of multiplicity, but with 3 distinct solutions, it has to be at least order 3.

i.e. (x - 1)(x - 1)(x - 1), has one distinct solution, x = 1, multiplicity 3.