Question

What is the least possible degree of a polynomial that has the root -3 + 2i, and a repeated root -2 that occurs twice? 2 3 4 5

Answer 1

is the answer 4 or 2

Explanation:

Answer 2

complex roots, never come all by their lonesome, their sister always comes along, so if there's a root of -3 + 2i, her sister the conjugate is also a root of such polynomial, namely -3 - 2i.

Now, if the -2 root has a multiplicity of 2, that is, is repeated twice, then, you're looking at the two complex roots and the two from the -2 root. So the polynomial will have at least 4 roots, two complex ones and two negative real ones.