Question

The Zero Product Property Quick Check
4 of 54 of 5 Items

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

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}.
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 .
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Answer 1

To solve the equation \( 0 = -13x(x - 6) \), we can use the Zero Product Property, which states that if the product of two factors is zero, then at least one of the factors must be zero.

Here, we have:
\[
-13x(x - 6) = 0
\]

We can set each factor equal to zero:

1. \( -13x = 0 \)
2. \( x - 6 = 0 \)

From the first equation, solving for \( x \):
\[
-13x = 0 \implies x = 0
\]

From the second equation, solving for \( x \):
\[
x - 6 = 0 \implies x = 6
\]

Thus, the solution set is:
\[
x = \{0, 6\}
\]

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