integer polynomial equation

Question

Write an integer polynomial equation (not in factor form) of lowest degree that has the zero 2i

 

Answer 1

The given zero is a complex number.  Complex numbers have conjugates.  So you will have 2 zero.

 

x₁ = 2i

x₂ = -2i

 

So your polynomial is

 

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

 

f(x) = x² + 4

 

 

If you were to graph this function, you will have a parabola that opens upward with a vertex of (0, 4).  This parabola does not intercept the x-axis.  Because of this, your roots are complex as given.