Question

How do you find a fourth degree polynomial given roots `2i` and `4-i`?

Answer 1

Assuming that the 4-th degree polynomial is of real coefficients, then the conjugates `-2i` and `4+i` are also roots

Explanation:

So we know the four roots of the polynomial, and then one of the possible polynomials is:

`(x-2i) * (x+2i) * ((x-(4-i)) * ((x-(4+i)) = (x^2-4) * (x^2-17) = x^4-4x^2-17x^2+68= x^4-21x^2+68`

So a possible answer is `x^4-21x^2+68`, but of course for any constant `k` also any polynomial

`k * (x^4-21x^2+68)` is also a solution