Chapter 9.4, Problem 5LC

To determine

An example to show the use of Zero Product Property in solving a quadratic equation.

Answer to Problem 5LC

The solution will be $m=7and\text{ m = -2}\text{.}$

Explanation of Solution

Given:

The equation to be solved is quadratic.

Calculation:

Let the quadratic equation be:

  $m^2-5m-14=0$

Finding the factors and then solving the equation using Zero Product Property:

  $\begin{array}{l}{m}^2-5m-14=0\\ m^2-7m+2m-14=0\\ \left(m^2-7m\right)+\left(2m-14\right)=0\\ m\left(m-7\right)+2\left(m-7\right)=0\\ \left(m-7\right)\left(m+2\right)=0\\ \text{Using Zero Product Property:}\\ m-7=0\text{ or m + 2 = 0}\\ m=7\text{ or m = -2}\end{array}$

The solution will be $m=7and\text{ m = -2}\text{.}$