Use the table to answer the question.

Question

(x + 3) (x + 4) = 0
x - 3 = 0 | x + 4 = 0
x = 3 | x = -4
While using the Zero Product Property to find the values of x that make the quadratic equation (x + 3) (x + 4) equals 0, Oliver completed the work provided in the table. Is Oliver’s work accurate?

Answer 1

Let's analyze the equation given: \((x + 3)(x + 4) = 0\).

Using the Zero Product Property, we set each factor equal to zero:

1. \(x + 3 = 0\)
2. \(x + 4 = 0\)

Now, we solve each equation:

1. From \(x + 3 = 0\): \[ x = -3 \]

2. From \(x + 4 = 0\): \[ x = -4 \]

So, the solutions to the equation \((x + 3)(x + 4) = 0\) are \(x = -3\) and \(x = -4\).

Now, let's look at Oliver's work. In the table, it shows:

• For \(x - 3 = 0\), Oliver concluded \(x = 3\), which is incorrect because \(x - 3\) is not one of the factors of the given equation.
• For \(x + 4 = 0\), Oliver concluded \(x = -4\), which is correct.

Overall, Oliver's work contains one correct root and one incorrect root. Therefore, his work is inaccurate. The correct roots for the quadratic equation \((x + 3)(x + 4) = 0\) are \(x = -3\) and \(x = -4\).