Question

What is the least possible degree of a polynomial that has roots -5, 1 + 4i, and -4i?

2,3,4, or 5

Answer 1

5, because -5 is a real solution, meaning it’s by itself. 1+4i and -4i are imaginary solutions, and all imaginary solutions, or “i”s have a pair. So the three solutions above, plus the two that go with the imaginary solutions all add up to 5. :)

Answer 2

Least possible degree of polynomial = 5

Explanation:

Here we have solutions -5, 1 + 4i, and -4i.

The solutions are 1 real and 2 imaginary.

Real solutions may or may not be with pair.

We know that complex solutions comes with two solutions a + ib and a - ib

So the all solutions of the polynomial are

-5 , 1+4i, 1-4i, -4i, and 4i

So minimum 5 solutions are there for this polynomial.

Polynomial with 5 solutions are of degree 5.

Least possible degree of polynomial = 5