Chapter 12, Problem 5CT

To determine

To calculate: The value of $z$ from the equation $3z^2-6z-9=0$ by the quadratic formula.

Answer to Problem 5CT

The values are $\left\{3,-1\right\}$ .

Explanation of Solution

Given information:

The expression is given as:

  $3z^2-6z-9=0$

Formula used:

If $a{z}^2+bz+c=0$ , $a\ne 0$ and $b^2-4ac\ge 0$ .

Then $z=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Calculation:

Using the quadratic formula,

The values of $a=3,b=-6\text{and}c=-9$ put into the quadratic formula,

  $\begin{array}{l}z=\frac{-\left(-6\right)\pm \sqrt{36-4\cdot 3\cdot \left(-9\right)}}{2\cdot 3}\\ z=\frac{6\pm \sqrt{36+108}}{6}\\ z=\frac{6\pm \sqrt{144}}{6}\end{array}$

Furthermore,

  $\begin{array}{l}z=\frac{6\pm 12}{6}\\ z=3\text{or}z=-1\end{array}$

The value of $z$ is $\left\{3,-1\right\}$ .