Question

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

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

The solution set is x={1/3,6}
.
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}
.
The solution set is x equals left brace neagtive 0 comma negative 6 right brace .

The solution set is x={−6,3}
.
The solution set is x equals left brace neagtive 6 comma 3 right brace .
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page 14 of 14

Answer 1

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 \(x = \{0, 6\}\).