Question

What is the polynomial function of lowest degree with lead coefficient 1 and roots i, –2, and 2?

Answer 1

Answer:

x^4 - 3x^2 - 4.

Step-by-step explanation:

Imaginary roots  occur as conjugate pairs  so a 4th roots is -i.

So in factor form we have:

f(x) = (x - 2)(x + 2)(x - i)x + i)

     = (x^2 + 1)(x - 2)(x + 2)

     = (x^2 + 1)(x^2 - 4)

      = x^4 - 3x^2 - 4.