Chapter 4.6, Problem 49E

To determine

To find:The complex roots of $12x^2+8x-15=0$ and the number of roots.

Answer to Problem 49E

The complex roots of the equation $12x^2+8x-15=0$ is $\frac{-3}{2},\frac{5}{6}$ and the number of roots are two.

Explanation of Solution

Given information:

The given information is equation $12x^2+8x-15=0$ .

To find the roots of the given equation it is necessary to factorise the equation.

Thus,

  $\begin{array}{c}12x^2+8x-15=0\\ \left(2x+3\right)\left(6x-5\right)=0\\ x=\frac{-3}{2},\frac{5}{6}\end{array}$

Now, the number of roots are two as the given equation is quadratic.

Therefore, the complex roots of the equation $12x^2+8x-15=0$ is $\frac{-3}{2},\frac{5}{6}$ and the number of roots are two.