Chapter 8.5, Problem 44E

To determine

To find:The zeros of the function.

Answer to Problem 44E

The zeros are: -4, -3 and 3

Explanation of Solution

Given information:

To finding the zero of the function as given below,

  $y=\left(x+4\right)\left(x^2-9\right)$

The zeros of the function are -4 and 9

Formula used:

The zeros of the function are obtained by equating the function to zero.

Calculation:

The error was in solving the equation $x^2-9=0$ in a wrong way. It was treated as a linear equation, but it is a quadratic equation which can be solved either directly with the square root method, or factoring the expression and applying the Zero- Product Property.

  $\begin{array}{l}\left(x+4\right)\left(x+3\right)\left(x-3\right)=0\\ x+4=0\text{or}x+3=0\text{or}x-3=0\\ x=-4\text{or }x=-3\text{or}x=3\end{array}$

The zeros are: -4, -3 and 3

Conclusion:

The zeros are: -4, -3 and 3