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

The solution set is x={213,34}
.

Answer 1

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

1. Set the first factor to zero: \[ 13x - 2 = 0 \] Solving for \(x\): \[ 13x = 2 \implies x = \frac{2}{13} \]

2. Set the second factor to zero: \[ x - 34 = 0 \] Solving for \(x\): \[ x = 34 \]

So the solutions are \(x = \frac{2}{13}\) and \(x = 34\).

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

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