Question

Write a polynomial function in standard form with the given roots: -4i

Answer 1

`f(x)=x^2+16`

Explanation:

By the conjugate rule, if -4i is a root, then so is +4i. So we have 2 roots, thus, we have a second degree polynomial (namely, a quadratic). If

x = -4i, then

x + 4i is a root.

If

x = 4i, then

x - 4i is a root.

Having (x - 4i)(x + 4i) as roots, we can now FOIL them together to get a polynomial of least degree.

FOILing gives us

`x^2+4ix-4ix-16i^2`

Notice that the +4ix and the -4ix cancel each other out, leaving you with

`x^2-16i^2`

Since

`i^2=-1`

we can make the substitution:

`x^2-16(-1)`

which simplifies to

`x^2+16`

In function notation form:

`f(x)=x^2+16`