https://file.aiquickdraw.com/mathbot/file/1725814031464am26qj3w.jpg

It appears that you've uploaded an image related to a quadratic equation problem. Based on what I can see, the equation provided is:

\[
2x^2 + 8x + 10 = 0
\]

You're asked to use Vieta's formulas to find the **sum** and **product** of the roots of this equation.

### Vieta's Formulas:
For a quadratic equation of the form \( ax^2 + bx + c = 0 \), Vieta's formulas tell us that:
- The **sum** of the roots \( (x_1 + x_2) \) is given by:
  \[
  \text{Sum of roots} = -\frac{b}{a}
  \]
- The **product** of the roots \( (x_1 \cdot x_2) \) is given by:
  \[
  \text{Product of roots} = \frac{c}{a}
  \]

### Applying Vieta's Formulas to \( 2x^2 + 8x + 10 = 0 \):
- \( a = 2 \), \( b = 8 \), and \( c = 10 \)
- The sum of the roots is:
  \[
  \text{Sum of roots} = -\frac{8}{2} = -4
  \]
- The product of the roots is:
  \[
  \text{Product of roots} = \frac{10}{2} = 5
  \]

Thus, the sum of the roots is **-4**, and the product of the roots is **5**.

Do you want more details or have any further questions?

Here are 5 related questions to expand your understanding:
1. How would you solve the quadratic equation using the quadratic formula?
2. What is the geometric interpretation of the sum and product of the roots?
3. How do the signs of \( b \) and \( c \) affect the roots of a quadratic equation?
4. Can Vieta’s formulas be applied to higher-degree polynomials?
5. What is the relationship between the discriminant and the nature of the roots?

**Tip:** Vieta's formulas are a powerful tool for quickly finding relationships between the coefficients of a polynomial and its roots without solving the equation explicitly.

Use Vieta's formulas to find the sum and the product of the roots of the equation 2x^2 + 8x + 10 = 0.

Learn how to use Vieta's formulas to find the sum and product of the roots of the quadratic equation 2x^2 + 8x + 10 = 0. This solution explains the application of algebraic concepts and formulas for students in Grades 8-10.

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