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

Question

Responses

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}.
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={0,6}.

Answer 1

To solve the equation \( 0 = -13x(x - 6) \), we first set the factored form equal to zero:

\[ -13x(x - 6) = 0 \]

This equation will be true if either factor is equal to zero:

1. Set the first factor to zero: \[ -13x = 0 \quad \Rightarrow \quad x = 0 \]

2. Set the second factor to zero: \[ x - 6 = 0 \quad \Rightarrow \quad x = 6 \]

Thus, the solutions to the equation are:

\[ x = 0 \quad \text{and} \quad x = 6 \]

The solution set can be expressed as:

\[ x = {0, 6} \]

Therefore, the correct response is:

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