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Let's work through the tables based on the given information. For both parts B and C, the quadratic equation can be written using the relationship between the roots, sum, and product of the quadratic.

For any quadratic equation of the form:

\[
x^2 - ( \text{sum of the roots}) x + (\text{product of the roots}) = 0
\]

### Part B:
We are given the sum and product of the roots, and we need to write the quadratic equations.

1. **Sum = 1, Product = 28**
   \[
   x^2 - (1)x + 28 = 0 \quad \Rightarrow \quad x^2 - x + 28 = 0
   \]

2. **Sum = -19, Product = -66**
   \[
   x^2 - (-19)x + (-66) = 0 \quad \Rightarrow \quad x^2 + 19x - 66 = 0
   \]

3. **Sum = 3, Product = 5**
   \[
   x^2 - 3x + 5 = 0
   \]

4. **Sum = 4, Product = 6**
   \[
   x^2 - 4x + 6 = 0
   \]

### Part C:
We are given the roots, and we need to calculate the sum, product, and write the quadratic equations.

1. **Roots = 6 and 3**
   \[
   \text{Sum} = 6 + 3 = 9, \quad \text{Product} = 6 \times 3 = 18
   \]
   \[
   x^2 - 9x + 18 = 0
   \]

2. **Roots = -3 and 15**
   \[
   \text{Sum} = -3 + 15 = 12, \quad \text{Product} = -3 \times 15 = -45
   \]
   \[
   x^2 - 12x - 45 = 0
   \]

3. **Roots = -9 and 0**
   \[
   \text{Sum} = -9 + 0 = -9, \quad \text{Product} = -9 \times 0 = 0
   \]
   \[
   x^2 + 9x = 0
   \]

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Would you like further explanations on any of these steps?

### Here are 5 related questions:
1. How do we derive the sum and product of roots from a quadratic equation?
2. How can we find the roots of a quadratic equation using the quadratic formula?
3. What happens when the product of the roots is zero in a quadratic equation?
4. How does changing the sum and product of roots affect the shape of the parabola?
5. Can we find the quadratic equation given only one root?

**Tip:** The discriminant \( \Delta = b^2 - 4ac \) tells us whether a quadratic equation has real or complex roots.

The problem involves completing tables to write quadratic equations based on the sum and product of the roots, or based on the given roots.

This math worksheet guides students through solving quadratic equations using the sum and product of the roots. Learn how to write quadratic equations in standard form and apply algebraic concepts. Suitable for Grades 8-10 students.

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