# How do you write a polynomial function in standard form with real coefficients whose zeros include #1#, #9i#, and #-9 i#?

##### 1 Answer

The simplest such polynomial is:

#f(x) = x^3-x^2+81x-81#

#### Explanation:

Given zeros

Any polynomial in

So let:

#f(x) = (x-1)(x-9i)(x+9i)#

#color(white)(f(x)) = (x-1)(x^2-(9i)^2)#

#color(white)(f(x)) = (x-1)(x^2+81)#

#color(white)(f(x)) = x^3-x^2+81x-81#

So this

**Footnote**

If only the zeros

One way to think of this is to recognise that