Chapter 4.2, Problem 39E

To determine

To Find: The member of complex roots of the equation $18a^2+3a-1=0$ and the graph for it.

Answer to Problem 39E

The required roots are $a=\frac{-1}{3},\frac{1}{6}$ and the graph of the function is shown in Figure 1

Explanation of Solution

The given equation is,

  $18a^2+3a-1=0$

Since, the degree of the polynomial is 2 so the number of complex root is 2 and is obtained as,

  $\begin{array}{l}18a^2+3a-1=0\\ 18a^2+6a-3a-1=0\\ 6a\left(3a+1\right)-\left(3a+1\right)=0\\ \left(3a+1\right)\left(6a-1\right)=0\end{array}$

Then,

  $a=\frac{-1}{3},\frac{1}{6}$

The graph of the function is shown in Figure 1

  

Figure 1