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Enter the product and sum values, and the calculator will determine the combination numbers of the quadratic equation formed, with the steps displayed.
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Our free Product Sum Calculator helps you determine two numbers given their product and sum. Whether you need exact values of variables (x, y) or a complete step-by-step solution, this calculator simplifies the process instantly.
Definition: In mathematics, the sum of products refers to calculations where multiplication is applied first, followed by addition, subtraction, or division as needed. When two numbers are known by their sum and product, you can find the numbers using algebraic methods.
You can verify your results using our online summation calculator.
Problem: Find two numbers with a product of 24 and a sum of 44.
Solution:
Substitute y into the product equation:
$$ x(44 - x) = 24 $$
$$ -x^2 + 44x - 24 = 0 $$
Rewrite in standard quadratic form:
$$ x^2 - 44x + 24 = 0 $$
Using the quadratic formula:
$$ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} $$
Where a = 1, b = -44, c = 24:
$$ x = \frac{44 \pm \sqrt{1936 - 96}}{2} $$
$$ x = \frac{44 \pm \sqrt{1840}}{2} $$
$$ x_1 \approx 43.4476, \quad x_2 \approx 0.5524 $$
Hence, the two numbers are approximately 43.4476 and 0.5524. You can confirm using the product sum calculator.
For further verification, you can use our Quadratic Formula Calculator.
The sum is the result of adding two or more numbers. Here, it is the value x + y.
The product is the result of multiplying two or more numbers. Here, it is the value xy.
In probability, the sum rule finds the chance of either of two mutually exclusive events, while the product rule finds the probability of both events occurring independently.
Using the Product Sum Calculator, you can quickly find two numbers from their sum and product. It is particularly useful for solving quadratic equations derived from real-life problems, offering accurate, step-by-step solutions.
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