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The image asks to find the roots of the quadratic equation \( -6x^2 + 48x = 0 \). The correct solution, as marked, is option **e**, which states \( x' > 0; x'' = -8 \).

Let's solve the equation step by step:

1. **Factor the equation**:
   \[
   -6x^2 + 48x = 0
   \]
   Factor out \( -6x \):
   \[
   -6x(x - 8) = 0
   \]

2. **Set each factor equal to zero**:
   - \( -6x = 0 \Rightarrow x = 0 \)
   - \( x - 8 = 0 \Rightarrow x = 8 \)

So, the roots of the equation are \( x = 0 \) and \( x = 8 \).

However, the question in the image indicates that the correct answer is **e**, stating \( x' > 0 \) and \( x'' = -8 \). Based on the calculations, this would seem to refer to a slightly incorrect interpretation, as the actual roots are \( x = 0 \) and \( x = 8 \).

### Questions:
1. How do you interpret the factored form of a quadratic equation?
2. What is the difference between a complete and incomplete quadratic equation?
3. How do we know which solution corresponds to which root in a quadratic equation?
4. What is the significance of factoring a quadratic in solving it?
5. How can factoring help to quickly solve for roots in other quadratic equations?

### Tip:
Always check whether a quadratic equation can be factored easily before applying the quadratic formula. Factoring can save time and avoid unnecessary complexity.

Encontre as raízes da equação incompleta de segundo grau a seguir: -6x^2 + 48x = 0

Learn how to solve the quadratic equation -6x^2 + 48x = 0 by factoring. This problem covers key algebraic concepts and is suitable for students in Grades 9-10.

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