What is the polynomial function of lowest degree with lead coefficient 1 and roots i, –2, and 2?
f(x) = x3 – x2 – 4x + 4
f(x) = x4 – 3x2 – 4
f(x) = x4 + 3x2 – 4
f(x) = x3 + x2 – 4x – 4

The polynomial function is given by:

We are given the roots of a polynomial function as:

          i, –2, and 2.

Also, the leading coefficient is: 1

We know that if for any polynomial function the complex number is a root of the polynomial then it's conjugate is also a root of the function.

i.e. here i is a root.

Hence, -i is also a root of the polynomial function.

The function will be given by:

Since, we know that:

Hence, we have:

( since,

)

Hence, we have: