How do you write a polynomial in standard form given zeros 5i and -5i?

1 Answer
Apr 15, 2016

Answer:

#x^2+25#

Explanation:

If #color(red)(5i)# and #color(blue)(-5i)# are zeros of a polynomial
then
#color(white)("XXX")(x-color(red)(5i))# and #(xcolor(blue)(+5i))# are factors of that polynomial.

The simplest polynomial with these factors will be the product of these (and only these) factors:
#color(white)("XXX")(x-5i)(x+5i) = x^2+25#