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The equation given is:

\[
x^2 + \frac{b}{a}x + \frac{c}{a} = 0
\]

This can be rewritten as a standard quadratic equation of the form:

\[
Ax^2 + Bx + C = 0
\]

Here, \( A = 1 \), \( B = \frac{b}{a} \), and \( C = \frac{c}{a} \).

For a quadratic equation \( Ax^2 + Bx + C = 0 \), we know the following properties about the roots:

1. **Sum of the roots**: 
   \[
   \text{Sum of roots} = -\frac{B}{A}
   \]
   In this case, \( B = \frac{b}{a} \) and \( A = 1 \), so:
   \[
   \text{Sum of roots} = -\frac{\frac{b}{a}}{1} = -\frac{b}{a}
   \]
   
2. **Product of the roots**:
   \[
   \text{Product of roots} = \frac{C}{A}
   \]
   In this case, \( C = \frac{c}{a} \) and \( A = 1 \), so:
   \[
   \text{Product of roots} = \frac{\frac{c}{a}}{1} = \frac{c}{a}
   \]

Now let's analyze the statements:

- **The product of its roots = \(\frac{c}{a}\)**: This is **correct**, based on the product formula.
- **The division of its roots = \(\frac{c}{a}\)**: This is **incorrect**. There is no standard formula for the "division" of roots.
- **The sum of its roots = \(-\frac{b}{a}\)**: This is **correct**, based on the sum formula.
- **The difference of its roots = \(-\frac{b}{a}\)**: This is **incorrect**. The difference of roots is not calculated this way and depends on the discriminant.

### Correct Answers:
- The product of its roots = \(\frac{c}{a}\)
- The sum of its roots = \(-\frac{b}{a}\)

Would you like more details or have any questions?

Here are 5 related questions you might consider:
1. What is the formula for the difference of roots in a quadratic equation?
2. How do we find the roots of a quadratic equation using the quadratic formula?
3. What is the relationship between the discriminant and the nature of the roots?
4. How does changing the values of \( a \), \( b \), and \( c \) affect the roots?
5. Can you derive the product and sum of roots using Vieta’s formulas?

**Tip:** Vieta's formulas give the sum and product of the roots directly from the coefficients of the quadratic equation.

Select all that apply.
If x^2 + (b/a)x + (c/a) = 0; then:

Understand the sum and product of the roots for the quadratic equation x^2 + (b/a)x + (c/a) = 0, using Vieta's formulas. Suitable for Grades 8-10 students learning quadratic equations.

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