How do you write a polynomial in standard form given the zeros x=5, 8i, and -8i?

1 Answer
Nov 2, 2016

Answer:

#f(x) = x^3-5x^2+64x-320#

Explanation:

We find the simplest such polynomial by multiplying the corresponding linear factors:

#f(x) = (x-5)(x-8i)(x+8i)#

#color(white)(f(x)) = (x-5)(x^2-(8i)^2)#

#color(white)(f(x)) = (x-5)(x^2+64)#

#color(white)(f(x)) = x^3-5x^2+64x-320#

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