1. What is the Product Sum Factor Calculator?

This calculator finds the two numbers (factors) that have a given product (P) and sum (S). These numbers are the roots of the quadratic equation x² - Sx + P = 0.

2. How Does the Calculator Work?

The calculator solves the quadratic equation:

Where:

• \( S \) — Sum of the two numbers
• \( P \) — Product of the two numbers

Explanation: The quadratic formula is used to find the roots, which represent the two numbers that satisfy both the sum and product conditions.

3. Mathematical Explanation

Details: For any two numbers with sum S and product P, they must satisfy the quadratic equation x² - Sx + P = 0. The roots can be real or complex depending on the discriminant (S² - 4P).

4. Using the Calculator

Tips: Enter the desired product (P) and sum (S) values. The calculator will display the two numbers (roots) that satisfy both conditions.

5. Frequently Asked Questions (FAQ)

Q1: What if the discriminant is negative?
A: The calculator will show complex roots in the form a ± bi when the discriminant is negative (S² < 4P).

Q2: Can this be used for factoring quadratics?
A: Yes, this is essentially the reverse process of factoring a quadratic equation.

Q3: What if P = 0?
A: When product is zero, one of the roots will be zero and the other will equal the sum S.

Q4: Are there practical applications?
A: This is useful in algebra problems, physics (projectile motion), economics (profit maximization), and many other fields.

Q5: How precise are the results?
A: Results are rounded to 4 decimal places for display, but calculations use full precision.