Sum and Product Calculator

Calculate the sum, product, difference, and quotient of two numbers, or find two numbers from their sum and product.

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Sum
13

Step-by-Step Solution

Sum and Product of Two Numbers

Given two numbers a and b, their sum (a + b) and product (a x b) are the most fundamental operations in arithmetic. These operations are commutative, meaning the order does not matter. Additionally, knowing the sum and product of two numbers uniquely determines the numbers themselves (up to order) via Vieta's formulas.

Key Formulas

Sum

The result of adding two numbers together.

S = a + b

Product

The result of multiplying two numbers together.

P = a x b

Reverse: Find a and b

Given S and P, solve the quadratic x^2 - Sx + P = 0.

x = (S +/- sqrt(S^2 - 4P)) / 2

Difference of Squares

Relates sum, difference, and product of two expressions.

(a+b)(a-b) = a^2 - b^2

Applications

  • Vieta's formulas connect roots of polynomials to their coefficients via sum and product.
  • Factoring quadratic expressions requires finding two numbers with a given sum and product.
  • Cryptographic algorithms rely on the difficulty of finding factors given a product.
  • Statistics uses sum and product for mean, variance, and correlation calculations.