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

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Answer 1 · 2017-04-30T15:29:35

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

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

How do you find a fourth degree polynomial given roots 2i2i and 4-i4-i?