Question

Which of these potential solutions make 3x2−27x=0
true?(1 point)
Responses

0 and 3
0 and 3

3 and 3
3 and 3

0 and −9
0 and negative 9

0 and 9

Answer 1

To solve the equation \( 3x^2 - 27x = 0 \), we can factor out the common term:

1. Factor out \( 3x \):
\[
3x(x - 9) = 0
\]

2. Set each factor equal to zero:
\[
3x = 0 \quad \text{or} \quad x - 9 = 0
\]

3. Solve each equation:
- From \( 3x = 0 \):
\[
x = 0
\]
- From \( x - 9 = 0 \):
\[
x = 9
\]

Thus, the solutions to the equation \( 3x^2 - 27x = 0 \) are \( x = 0 \) and \( x = 9 \).

Among the provided options, the correct one is:

**0 and 9**.