Chapter 8.6, Problem 6OE

To determine

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

Answer to Problem 6OE

The other root is $\left(2+i,-2-i\right)$

Explanation of Solution

Given information:

The root is given as $2-i,-2+i$

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 $2+i$ ,the conjugate of $2-i$ and $-2-i$ , the conjugate of $-2+i$

Therefore,

The other root is $\left(2+i,-2-i\right)$