Question

Solve the quadratic equation (x+6)(x−4)=0 using the Zero Product Property.(1 point) Responses The solution set is {−6, 4} . The solution set is {−6, 4} . The solution set is {−4, 6} . The solution set is {−4, 6} . The solution set is {0, 2} . The solution set is {0, 2} . There are no solutions to this equation.

Answer 1

To solve the quadratic equation \((x+6)(x−4)=0\) using the Zero Product Property, we set each factor equal to zero:

1. \(x + 6 = 0\)
2. \(x - 4 = 0\)

Now, solve each equation:

1. For \(x + 6 = 0\):
\[
x = -6
\]

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

Thus, the solution set is \(\{-6, 4\}\).

The correct response is: The solution set is \(\{-6, 4\}\).