Chapter A.7, Problem 73AYU

To determine

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

Explanation of Solution

Given information:

The equationis $3x^2-3x+4=0$ .

Calculation:

Consider the equation.

  $3x^2-3x+4=0$

Check for $b^2-4ac$ ,

  $\begin{array}{c}{\left(-3\right)}^2-4\left(3\right)\left(4\right)=9-48\\ =-39\end{array}$

As $b^2-4ac<0$ , there are two complex solutions which are conjugates of each other.