Solve the quadratic equation 5x(x+12)=0

Question

using the Zero Product Property.(1 point)
Responses

The solution set is x={0, 12}
.
The solution set is x={0, 12}
.

The solution set is x={5, 12}
.
The solution set is x={5, 12}
.

The solution set is x={112, 15}
.
The solution set is x={112, 15}
.

The solution set is x={−12, 0}
.

Answer 1

To solve the quadratic equation \(5x(x + 12) = 0\) using the Zero Product Property, we start by setting each factor equal to zero.

The equation \(5x(x + 12) = 0\) breaks down into two factors:

1. \(5x = 0\)
2. \(x + 12 = 0\)

Now, we solve each factor:

1. From \(5x = 0\): \[ x = 0 \]

2. From \(x + 12 = 0\): \[ x = -12 \]

Thus, the solutions to the equation are \(x = 0\) and \(x = -12\).

The solution set is \(x = {-12, 0}\).

So, the correct response is:

The solution set is x={−12, 0}.