Question

Find the polynomial function of least degree with real coefficients in standard form that has the zeros 2,3i, and -3i. (Write the factors and multiply.)

Answer 1

`f(x)=x^3-2x^2+9x-18`

Step-by-step explanation:

If the zeroes of the polynomial function are: 2, 3i, and -3i.

We have that:

`x=2,x=3i,x=-3i`

This implies that:

`\begin{gathered} x-2=0\text{ or }x-3i=0\text{ or }x+3i=0 \\ \implies(x-2)(x-3i)(x+3i)=0 \end{gathered}`

We multiply the factors

`\begin{gathered} (x-2)(x^2-9i^2)=0 \\ (x-2)(x^2+9)=0 \\ x^3+9x-2x^2-18=0 \\ x^3-2x^2+9x-18=0 \end{gathered}`

The polynomial function therefore is:

`f(x)=x^3-2x^2+9x-18`