How do you write the polynomial function with the least degree and zeroes i, 4?

2 Answers

The requested polynomial is

#(x-i)(x-4)=x^2-x(4+i)+4i=0#

Sep 12, 2015

Answer:

If the polynomial is also to have Real coefficients, then it must also have #-i# as a zero, so:

#f(x) = (x-i)(x+i)(x-4) = (x^2+1)(x-4)#

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

Explanation:

Complex roots of polynomial equations with Real coefficients always occur in conjugate pairs.

Note that any polynomial that has these roots will be a multiple (scalar or polynomial) of #f#.