Solve the factored quadratic equation 0=−13x(x−6) .(1 point) 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={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={13,6}. The solution set is x equals left brace Start Fraction 1 over 3 End Fraction comma 6 right brace .

Question

GPT-4o mini · Answer

To solve the factored quadratic equation \( 0 = -13x(x - 6) \), we can start by setting the equation equal to zero:

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

This equation will be true if either factor is zero. Thus, we can set each factor equal to zero:

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

Solving the first factor:

\[ -13x = 0 \implies x = 0 \]

Solving the second factor:

\[ x - 6 = 0 \implies x = 6 \]

Thus, the solutions to the equation are:

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

Therefore, the solution set is

\[ {0, 6} \]

So the correct response is:

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