find the sum and the product form that has given the roots r+s=5/2, rs=1

Given the roots \( r \) and \( s \) of a quadratic equation, we know:

- The sum of the roots, \( r + s = \frac{5}{2} \)
- The product of the roots, \( rs = 1 \)

To find the quadratic equation, we use the standard form:

\[
x^2 - (r+s)x + rs = 0
\]

Substituting the given values:

\[
x^2 - \left(\frac{5}{2}\right)x + 1 = 0
\]

So the quadratic equation is:

\[
x^2 - \frac{5}{2}x + 1 = 0
\]

### Summary:
- **Sum form**: \( x^2 - \frac{5}{2}x + 1 = 0 \)
- **Product form**: The expression above is in the expanded standard form, which is also the "product form" in this context.

Would you like more details or have any questions? 

Here are 5 related questions to explore further:
1. How would you convert this equation into a different form, like vertex form?
2. What are the roots of the equation \(x^2 - \frac{5}{2}x + 1 = 0\)?
3. How does changing the sum or product affect the roots of a quadratic equation?
4. What is the discriminant of this quadratic equation and what does it indicate?
5. How can you derive the quadratic formula using this specific equation?

**Tip:** When working with quadratic equations, always remember that the sum and product of the roots can be directly used to write the equation. This is a quick way to check your work or create equations from given roots.

Understand how to find the sum and product of roots in quadratic equations using Vieta's formulas. Explore a detailed solution example with given roots r+s=5/2 and rs=1. Suitable for Grades 9-12.

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