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

Answer 1

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

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

To find the solutions, we can set each factor equal to zero.

1. The term \( -\frac{1}{3} \) does not affect the solutions since it is a non-zero constant.

2. Setting the first factor \( x = 0 \): \[ x = 0 \]

3. Setting the second factor \( x - 6 = 0 \): \[ x - 6 = 0 \implies x = 6 \]

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

Therefore, the solution set is \( x = {0, 6} \).

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