Chapter 11 - Quadratic Functions and Equations - 11.3 Studying Solutions of Quadratic Equations - 11.3 Exercise Set - Page 718: 45

$$x^2+16$$

To write a quadratic equation with the given values as solutions, we find the corresponding factors. We then FOIL out the factors to find the original quadratic equation: $$ \left(x-4i\right)\left(x+4i\right)\\ x^2+\left(-4\right)^2\\ x^2+16$$