# How do you write a polynomial function of least degree and leading coefficient 1 when the zeros are 2i, -2i?

Sep 14, 2016

$f \left(x\right) = {x}^{2} + 4$

#### Explanation:

Let $f \left(x\right)$ be the polynomial of degree 2 and leading coefficient 1 with zeros $\pm 2 i$

Hence either $\left(x + 2 i\right)$ or $\left(x - 2 i\right) = 0$

$\therefore f \left(x\right) = 0 = \left(x + 2 i\right) \left(x - 2 i\right)$

$f \left(x\right) = {x}^{2} + 2 i x - 2 i x - 4 {i}^{2}$

$f \left(x\right) = {x}^{2} + 4$