Chapter 12, Problem 5CR

To determine

To define: The correct option of expression $5z^2+11z+2=0$ ,solve by quadratic formula and the options are,

  $\begin{array}{l}\text{a}.\left\{-2,\frac{-1}{5}\right\}\\ \text{b}\text{.}\left\{2,\frac{1}{5}\right\}\\ \text{c}.\left\{2,\frac{-1}{5}\right\}\\ \text{d}\text{.}\text{}\left\{-2,\frac{1}{5}\right\}\end{array}$

Answer to Problem 5CR

The correct option of expression $5z^2+11z+2=0$ is $\text{a}.\left\{-2,\frac{-1}{5}\right\}$ .

Explanation of Solution

Given information:

The expression $5z^2+11z+2=0$ and provided options are,

  $\begin{array}{l}\text{a}.\left\{-2,\frac{-1}{5}\right\}\\ \text{b}\text{.}\left\{2,\frac{1}{5}\right\}\\ \text{c}.\left\{2,\frac{-1}{5}\right\}\\ \text{d}\text{.}\text{}\left\{-2,\frac{1}{5}\right\}\end{array}$

The provided expression is $5z^2+11z+2=0$ now solve for the value of $z$ by the quadratic formula.

Quadratic formula,

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

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

Using the quadratic formula,

The values of $a=5,b=11\text{and}c=2$ put into the quadratic formula,

  $\begin{array}{l}z=\frac{-11\pm \sqrt{121-4\cdot 5\cdot 2}}{2\cdot 5}\\ z=\frac{-11\pm \sqrt{81}}{10}\\ z=\frac{-11\pm 9}{10}\end{array}$

Furthermore,

  $\begin{array}{l}z=\frac{-11\pm 9}{10}\\ z=-2\text{or}z=\frac{-1}{5}\end{array}$

The value of $z$ is $\left\{-2,\frac{-1}{5}\right\}$ .

Thus, the option $\text{a}$ is correct.