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

Question

.(1 point)
Responses

The solution set is x={2,34}
.
The solution set is x equals left brace 2 comma 34 right brace .

The solution set is x={132,34}
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The solution set is x equals left brace Start Fraction 13 over 2 End Fraction comma 34 right brace .

The solution set is x={213,34}
.
The solution set is x equals left brace Start Fraction 2 over 13 End Fraction comma 34 right brace .

The solution set is x={−34,−213}
.

Answer 1

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

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

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

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

So the solutions are: \[ x = \frac{2}{13} \quad \text{and} \quad x = 34 \]

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

The correct response from your options is: The solution set is \( x = \left{ \frac{2}{13}, 34 \right} \).