Question

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

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}.
The solution set is x equals left brace 0 comma 6 right brace .

The solution set is x={−6,3}.

Answer 1

To solve the factored quadratic equation 0 = −13x(x−6), we use the zero product property, which states that if a product of two factors is zero, then at least one of the factors must be zero. Therefore, we can set each factor equal to zero and solve for x.

Setting the first factor equal to zero:
−13x = 0
Dividing both sides by -13, we get:
x = 0

Setting the second factor equal to zero:
x - 6 = 0
Adding 6 to both sides, we get:
x = 6

The solution set includes both values of x that make the equation true, which are x = 0 and x = 6.

Therefore, the correct solution set is x = {0, 6}.