Chapter A.7, Problem 76AYU

To determine

To explain:The character of solution of given equation in complex number system.

Explanation of Solution

Given information:

The equationis $x^2+6=2x$ .

Calculation:

Consider the equation.

  $\begin{array}{l}{x}^2+6=2x\\ x^2+6-2x=0\end{array}$

Check for $b^2-4ac$ ,

  $\begin{array}{c}{\left(-2\right)}^2-4\left(1\right)\left(6\right)=4-24\\ =-20\end{array}$

As $b^2-4ac<0$ , there are two complex solution that are conjugate of each other.