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To find the sum and product of the roots of the equation \(5x^2 - 4x - 17 = 0\), we can use the relationships from Vieta’s formulas. For a quadratic equation of the form \(ax^2 + bx + c = 0\), the following holds:

1. **Sum of the roots** \((r_1 + r_2) = -\frac{b}{a}\)
2. **Product of the roots** \((r_1 \cdot r_2) = \frac{c}{a}\)

In this equation:
- \(a = 5\),
- \(b = -4\), and
- \(c = -17\).

### Calculations
1. **Sum of the roots:**
   \[
   r_1 + r_2 = -\frac{-4}{5} = \frac{4}{5}
   \]

2. **Product of the roots:**
   \[
   r_1 \cdot r_2 = \frac{-17}{5} = -\frac{17}{5}
   \]

### Answer
- The sum of the roots is \(\frac{4}{5}\).
- The product of the roots is \(-\frac{17}{5}\).

Would you like further details or explanations on this? 

Here are some related questions:
1. How do Vieta’s formulas help in solving quadratic equations?
2. What happens to the sum and product if \(a\) changes but \(b\) and \(c\) remain the same?
3. Can the sum and product be used to reconstruct the original equation?
4. How would this process change if the equation had complex roots?
5. What are other methods to find the roots of a quadratic equation?

**Tip:** Remember, Vieta’s formulas are useful shortcuts for identifying relationships between the coefficients and the roots without solving the equation.

Find the sum and the product of the roots of the equation 5x^2 - 4x - 17 = 0.

Learn how to find the sum and product of the roots of the quadratic equation 5x^2 - 4x - 17 = 0 using Vieta's formulas. This problem demonstrates key algebraic concepts in quadratic equations, ideal for students in Grades 9-11.

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