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={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 .

The solution set is x={13,6}.

Answer 1

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

1. First, observe that the equation can be rewritten as:

\[
-\frac{1}{3}x(x - 6) = 0
\]

2. Since the product of the factors equals zero, we can set each factor equal to zero:

\[
x = 0
\]
\[
x - 6 = 0 \quad \Rightarrow \quad x = 6
\]

Thus, the solutions are \( x = 0 \) and \( x = 6 \).

The solution set is:

\[
x = \{0, 6\}
\]

Hence, the correct response is:

**The solution set is \( x = \{0, 6\} \).**