Question

Solve the factored quadratic equation (19x−3)(9+x)=0
(1 point)
Responses

{193,9}
start set 19 thirds comma 9 end set

{−9,319}
start set negative 9 comma 3 over 19 end set

{−9, 3}
{−9, 3}

{−9,193}

Answer 1

To solve the factored quadratic equation \((19x−3)(9+x)=0\), we set each factor equal to zero:

1. Set the first factor equal to zero:
\[
19x - 3 = 0
\]
\[
19x = 3
\]
\[
x = \frac{3}{19}
\]

2. Set the second factor equal to zero:
\[
9 + x = 0
\]
\[
x = -9
\]

Thus, the solutions to the equation are:
\[
x = \frac{3}{19} \quad \text{and} \quad x = -9
\]

In set notation, the answer is:
\[
\left\{-9, \frac{3}{19}\right\}
\]

Among the provided responses, the correct solution is represented as:
\[
\{−9, 3/19\}
\]

So, choose \(\{-9, 3/19\}\) as the correct answer.