How do you write a polynomial function of least degree with integral coefficients that has the given zeroes 6, 2i?

1 Answer
Jul 17, 2016

Answer:

#f(x) = x^3-6x^2+4x-24#

Explanation:

If a polynomial has Real coefficients then any non-Real zeros will occur in Complex conjugate pairs. So if #2i# is a zero, then so is #-2i#.

Hence our polynomial function can be written:

#f(x) = (x-6)(x-2i)(x+2i)#

#= (x-6)(x^2+4)#

#= x^3-6x^2+4x-24#

Any polynomial in #x# with these zeros will be a multiple (scalar or polynomial) of this #f(x)#