Solve the factored quadratic equation 0=−1/3x(x−6)

.(1 point)
Responses

The solution set is x={0,6}
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The solution set is x equals left brace 0 comma 6 right brace .

The solution set is x={1/3,6}
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The solution set is x equals left brace Start Fraction 1 over 3 End Fraction comma 6 right brace .

The solution set is x={0,−6}
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The solution set is x equals left brace neagtive 0 comma negative 6 right brace .

The solution set is x={−6,3}
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The solution set is x equals left brace neagtive 6 comma 3 right brace .
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User Icon for Bot GPT 4-o mini Bot GPT 4-o mini answered
2 hours ago

To solve the factored quadratic equation \(0 = -\frac{1}{3}x(x - 6)\), we can set each factor equal to zero:

  1. The first factor: \[ -\frac{1}{3}x = 0 \] To solve for \(x\): \[ x = 0 \]

  2. The second factor: \[ x - 6 = 0 \] To solve for \(x\): \[ x = 6 \]

Thus, the solutions to the quadratic equation are: \[ x = 0 \quad \text{and} \quad x = 6 \]

Therefore, the solution set is: \[ {0, 6} \]

The correct response is: The solution set is \(x = {0, 6}\).