Question

Write a polynomial of degree THREE in EXPANDED form with roots:x = -2i, x = 3No need to write f(x)

Answer 1

A polynomial with roots A, B, and C can be written as it follows:

`f(x)=(x-A)(x-B)(x-C)`

Because every time a complex number is the root of a polynomial, it's conjugated also is, let the roots A, B, and C stands for -2i, +2i, and 3, respectively. So, we can write the polynomial as follows:

`f(x)=(x-A)^{}(x-B)(x-C)=(x-(-2i))(x-2i)^{}(x-3)`

Now, we just need to make the calculation needed to reach the expanded form:

`\begin{gathered} f(x)=(x+2i)(x-2i)(x-3) \\ =(x^2-(2i)^2)(x-3)=(x^2+4)(x-3) \\ =x^3-3x^2+4x-12 \end{gathered}`

The answer to the present question is the following polynomial:

`x^3-3x^2+4x-12`