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.