Chapter 4.1, Problem 44E

To determine

To state: the number of complex roots of $6c^3-3c^2-45c=0$ and then find the roots and graph.

Answer to Problem 44E

There are 3 complex roots: $0+0i,-\frac{5}{2}+0i,3+0i$ .

  

Explanation of Solution

Given information: $6c^3-3c^2-45c=0$

Calculation:

  $\begin{array}{l}6c^3-3c^2-45c=0\\ 3c\left(2c^2-c-15\right)=0\\ 3c\left(2c+5\right)\left(c-3\right)=0\end{array}$

There are 3 complex roots: $0+0i,-\frac{5}{2}+0i,3+0i$

The graph