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

1 Answer
Apr 30, 2017

Answer:

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