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

Question

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

GPT-4o mini · Answer

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

The first factor is \( -13x \): \[ -13x = 0 \] Dividing both sides by -13 gives: \[ x = 0 \]
The second factor is \( (x - 6) \): \[ x - 6 = 0 \] Adding 6 to both sides gives: \[ x = 6 \]

Gathering both solutions, we find the solution set is: \[ x = {0, 6} \]

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