Chapter 8.6, Problem 4OE

To determine

To find: The other root(s) of the polynomial equation.

Answer to Problem 4OE

The other root is $\left(-3i,\frac{1}{3}i\right)$

Explanation of Solution

Given information:

The root is given as $3i,-\frac{1}{3}i$

Concept used:

Conjugate theorem,

If p is a polynomial in one variable with real coefficients, and $a+bi$ is a root of P with a and b real numbers, then its complex conjugate is $a-bi$ is also a root of P.

The other root(s) can be find as:

The other roots must be $-3i$ ,the conjugate of $3i$ and $+\frac{1}{3}i$ , the conjugate of $-\frac{1}{3}i$

Therefore,

The other root is $\left(-3i,\frac{1}{3}i\right)$