How do you write a polynomial function of least degree and leading coefficient #1# when the zeros are #4i#, #-4i#?

1 Answer
Feb 25, 2018

Answer:

#f(x) = x^2+16#

Explanation:

If #x=a# is a zero of a polynomial, then #(x-a)# is a factor.

Hence to get the required zeros we can write:

#f(x) = (x-4i)(x+4i)#

#color(white)(f(x)) = x^2-(4i)^2#

#color(white)(f(x)) = x^2+16#

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