Solve the factored quadratic equation 0=−13x(x−6) .(1 point)

Question

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={13,6}.
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}.

Answer 1

To solve the factored quadratic equation \( 0 = -13x(x - 6) \), we can set each factor equal to zero.

1. Set the first factor equal to zero: \[ -13x = 0 \] This simplifies to: \[ x = 0 \]

2. Set the second factor equal to zero: \[ x - 6 = 0 \] This simplifies to: \[ x = 6 \]

Now, we have two solutions: \( x = 0 \) and \( x = 6 \).

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

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