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 $\text{Sum} = -9 + 0 = -9, \quad \text{Product} = -9 \times 0 = 0$ $x^2 + 9x = 0$

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.