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

Question

0
=
−
1
3
𝑥
(
𝑥
−
6
)
.(1 point)
Responses

The solution set is x={−6,3}
𝑥
=
{
−
6
,
3
}
.
The solution set is x equals left brace neagtive 6 comma 3 right brace .

The solution set is x={13,6}
𝑥
=
{
1
3
,
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}
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}
𝑥
=
{
0
,
6
}
.
The solution set is x equals left brace 0 comma 6 right brace .

Answer 1

To solve the given factored quadratic equation:

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

First, we can set each factor of the equation to zero:

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

For the first equation: \[-13x = 0 \implies x = 0\]

For the second equation: \[x - 6 = 0 \implies x = 6\]

Thus, the solutions to the equation are: \[x = 0\] and \[x = 6\]

Therefore, the solution set is: \[{0, 6}\]

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