How do you write a polynomial with zeros 8, -i, i and leading coefficient 1?

1 Answer
Mar 2, 2017

color(green)(x^3-8x^2+x-8)

Explanation:

If the polynomial has zeros 8, -i, and i
then it has factors cxx(x-8)(x+i)(x-i) where c is a constant.

Since we are asked for a polynomial with a leading coefficient of 1,
c=1 and we can ignore it from here on.

color(blue)((x+i)(x-i))=x^2-i^2=x^2-(-1)=color(blue)(x^2+1)
and
(x-8)color(blue)((x+i)(x-i))=(x-8)xxcolor(blue)(""(x^2+1))=x^3-8x^2+x-8