How do you write a polynomial with zeros 8,-i, i?

1 Answer
Feb 11, 2016

Answer:

This polynomial is #(x^3 - 8x^2 + x - 8)#

Explanation:

We can use the factored form of polynomials to write this first, then FOIL it out into the STANDARD FORM.

since the polynomial has 3 given zeroes, we can write

#(x-8)(x+i)(x-i)#
We do this because letting x = 8,-i, or i would mean that the polynomial becomes (with an intended name) zero.

Now we can just distribute it out.

First do the two complex zeroes
#(x+i)(x-i) = x^2 - i^2#
#i^2 = -1#
so #x^2 - i^2# becomes #x^2 + 1#
Now, just FOIL out #(x-8)(x^2+1)#

#(x^3 - 8x^2 + x - 8)#
And we are done.