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Product Sum Calculator

Product Sum Calculator

Enter the values of product and sum and the calculator will determine product and sum combination numbers of the quadratic equation formed, with the steps shown.

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Product:

Sum:

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This free product sum calculator helps you to calculate the two numbers that have a product and the sum of the numbers in variables (x,y). Whether you want to compute values regarding product and sum of the numbers with a complete solution, you can use our sum of products calculator.

What is Product Sum in Math?

“The sum of products corresponding ranges or arrays are where multiplication is default but addition, subtraction, and division is also possible”.

Formula of sum and product:

The formula for the sum and product of roots is given as:

  • The sum of the roots = -b/a
  • The product of the roots = c/a

How to find Numbers for the given product and sum?

Go through the below procedure to estimate the Product and Sum of the given numbers.

  • In order to find what two numbers have a Product Sum, suppose the variables that you know initially.
  • Let’s consider the values you need to find are x, y whose product and sum are known.
  • Once you suppose the variables, write the given data in the form of equations.
  • By using the basic substitution method, you will get a term from which you can determine the values easily.

If you aren’t sure whether the results arrived are accurate or not, you can use this sum product rule calculator to check the results.

Besides, you can also determine the sum of specified numbers, series, or functions with the assistance of an online double summation calculator.

Solved Example:

For a better understanding of the concept, we will discuss an example of how to resolve the problem to find the Product and Sum.

Example:

What two numbers have a Product of 24 and a sum of 44?

Solution:

Given Product of two numbers = 24
Sum of two numbers = 44

Let’s assume the numbers you need to find as x and y.

Product(x.y) = 24

Sum(x+y) = 44

y = 44 – x

Substitute y in x.y = 24

Substitute the value of y in the equation x.y=24. It’s not important y if you want you to interchange with the value of x too as x and y are substitutable.

x. (44-x)=24

On solving the equation, the result of two numbers as 2 and 22

Hence the two numbers whose product is 24 and the sum is 44 are 2, 22.

Standard form: 1x^2 -44x + 24 = 0

Using the Quadratic Formula where

a = 1, b = -44, and c = 24

$$ x = \frac{ -b \pm \sqrt{b^2 – 4ac}}{ 2a } $$

$$ x = \frac{ – (-44) \pm \sqrt{(-44)^2 – 4(1)(24)}}{ 2(1) } $$

$$ x = \frac{ 44 \pm \sqrt{ 1936 – 96}}{ 2 } $$

$$ x = \frac{44 \pm \sqrt{1840}}{2} $$

As \(b^{2}−4ac > 0\), there are two real roots.

$$ x₁ = \frac{ 44 + \sqrt{1840}}{ 2 },x₁ = { 43.4476} $$

$$ x₂ = \frac{ 44 – \sqrt{1840}}{ 2 } \hspace{0.25in} and \hspace{0.25in} x₂ = { 0.5524} $$

You can verify this answer with our sum of numbers calculator.

How does the Product Sum Calculator work?

This free sum of products calculator is simple to use. Just enter the following inputs and make your calculations swiftly.
Input:

  • Enter the product of the number
  • Now go for entering the sum of number the same way
  • Now tap the calculate button

Output:
This product and sum calculator does the following calculations:

  • Determine the roots of the quadratic equation resulting from the product and sum being provided

An online quadratic formula calculator helps to solve a given quadratic equation by using the quadratic equation formula.

FAQ’s:

What is meant by Sum?

The sum is generally the result of adding two or more numbers in maths. Here you can calculate the values of sum and product by using this product sum calculator.

What is product in maths?

The product in maths is the result of multiplying two or more numbers.

Where do I get the procedure to find numbers given their Product and Sum?

You can use our sum and product calculator to find numbers with step-by-step solutions.

What is the sum product rule?

The sum rule is to find the probability of either of two events that cannot occur simultaneously. While the product rule is for finding the probability of both two events that are independent.

Conclusion:

Whether you want to know variables (x,y), you will need to calculate the term using 2 given numbers. When these numbers are multiplied together, they are the product of the variables of the a and c terms, and the sum of the term is -b and a. Using our product sum calculator with a complete solution, you can find these two integers.

Reference:

From the source of Wikipedia: Sum-product number, Sum-product numbers, and cycles of Fb for specific b
From the source of support.microsoft.com: SUMPRODUCT function