To turn the given sum and product into a quadratic equation, we can use the relationships between the roots of a quadratic equation and its coefficients.

For a quadratic equation of the form:

$x^2 - ( \text{sum of the roots}) \cdot x + (\text{product of the roots}) = 0,$

where:

• The sum of the roots is $5$.
• The product of the roots is $7$.

Substituting these values into the formula:

$x^2 - 5x + 7 = 0.$

So, the quadratic equation is:

$x^2 - 5x + 7 = 0.$

Would you like a detailed explanation, or do you have any questions?

Here are some related questions you might find useful:

1. How do you find the roots of a quadratic equation?
2. What is the significance of the discriminant in a quadratic equation?
3. How can you verify if a given quadratic equation has real or complex roots?
4. What are the different methods to solve a quadratic equation?
5. How do sum and product of roots change when the quadratic equation is modified?

Tip: Always remember that the sum and product of the roots directly relate to the coefficients of the quadratic equation in the form $ax^2 + bx + c = 0$.