How do you write a polynomial in standard form given zeros -1, 2, and 1 - i?

1 Answer
Aug 5, 2016

Answer:

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

Explanation:

Assuming that we want the polynomial to also have Real coefficients, any non-Real zeros will occur in Complex conjugate pairs. So if #1-i# is a zero then #1+i# is a zero too.

The simplest polynomial in #x# with zeros #-1#, #2#, #1-i# and #1+i# is:

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

#=(x^2-x-2)((x-1)^2-i^2))#

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

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

graph{x^4-3x^3+2x^2+2x-4 [-10, 10, -5, 5]}