Question

Solve the factored quadratic equation (13x−2)(x−34)=0
Responses

The solution set is x={−34,−2/13}
The solution set is x={2,34}
The solution set is x={2/13,34}
The solution set is x={13/2,34}

Answer 1

To solve the factored quadratic equation \((13x - 2)(x - 34) = 0\), we set each factor equal to zero:

1. \(13x - 2 = 0\)
2. \(x - 34 = 0\)

**Solving the first equation:**
\[
13x - 2 = 0 \\
13x = 2 \\
x = \frac{2}{13}
\]

**Solving the second equation:**
\[
x - 34 = 0 \\
x = 34
\]

Thus, the solution set is:
\[
x = \left\{ \frac{2}{13}, 34 \right\}
\]

So the correct response is:
**The solution set is x={2/13, 34}.**