sum=5 product=7 turn this into quadratic equation

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 \(ax^2 + bx + c = 0\).

Learn how to create a quadratic equation given the sum (5) and product (7) of its roots. This guide explains the core concepts of algebra and quadratic equations, including the relationship between coefficients and roots. Perfect for students in Grades 8-10.

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