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We are given the quadratic function \( f(x) = x^2 - 3x \) and asked to determine the roots of this equation.

To find the roots, we solve \( f(x) = 0 \), meaning:

\[
x^2 - 3x = 0
\]

This equation can be factored:

\[
x(x - 3) = 0
\]

From this, we have two possibilities:

1. \( x = 0 \)
2. \( x - 3 = 0 \) which gives \( x = 3 \)

So, the roots are \( x_1 = 0 \) and \( x_2 = 3 \).

Now, let's check which answer option matches these roots:

- Option A: \( x_1 = -3 \) and \( x_2 = -3 \) → Incorrect.
- Option B: \( x_1 = 0 \) and \( x_2 = -3 \) → Incorrect.
- Option C: \( x_1 = 2 \) and \( x_2 = 0 \) → Incorrect.
- Option D: \( x_1 = 0 \) and \( x_2 = 3 \) → Correct.
- Option E: \( x_1 = -3 \) and \( x_2 = -6 \) → Incorrect.

Thus, the correct answer is **Option D**.

Would you like more details or have any further questions?

Here are five related questions:
1. How do you solve quadratic equations using the quadratic formula?
2. Can every quadratic equation be factored easily?
3. What is the significance of the discriminant in quadratic equations?
4. How do you graph the function \( f(x) = x^2 - 3x \)?
5. How do the roots of a quadratic equation relate to its graph?

**Tip:** Always try factoring first when solving quadratic equations, as it can be quicker than using the quadratic formula if the equation is easily factorable.

Se f(x) = x^2 - 3x, então as raízes dessa equação serão definidas por:

Learn how to find the roots of the quadratic equation f(x) = x^2 - 3x by factoring. This solution covers key algebraic concepts, including factoring and the zero-product property. Suitable for students in Grades 8-10.

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