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

Question

.(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={1/3,6}
.

Answer 1

To solve the factored quadratic equation \( 0 = -\frac{1}{3}x(x - 6) \), we can first set the expression on the right side to zero:

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

This can be simplified by multiplying both sides by \(-3\), resulting in:

\[ x(x - 6) = 0 \]

Next, we can set each factor equal to zero:

1. \( x = 0 \)
2. \( x - 6 = 0 \) → \( x = 6 \)

Thus, the solution set is:

\[ x = {0, 6} \]

The correct response is:

The solution set is x={0,6}.