# How do you find a polynomial function that has zeros #2, 4+sqrt5, 4-sqrt5#?

##### 1 Answer

#### Explanation:

If

So the simplest polynomial function of

#f(x) = (x-2)(x-(4+sqrt(5)))(x-(4-sqrt(5)))#

#color(white)(f(x)) = (x-2)((x-4)+sqrt(5))((x-4)-sqrt(5))#

#color(white)(f(x)) = (x-2)((x-4)^2-5)#

#color(white)(f(x)) = (x-2)(x^2-8x+16-5)#

#color(white)(f(x)) = (x-2)(x^2-8x+11)#

#color(white)(f(x)) = x^3-10x^2+27x-22#

Any polynomial in

**Footnote**

In this example, we were asked for a function with zeros including both