Diamond Problems Flashcard

Front

What is the relationship between the sum and product of two numbers in a diamond problem?

Back

The sum of two numbers is the result of adding them together, while the product is the result of multiplying them. In diamond problems, these two values are used to find the two unknown numbers.

Front

How do you find two numbers given their sum and product?

Back

To find two numbers given their sum (S) and product (P), you can set up the equations x + y = S and xy = P. Then, solve for x and y using methods such as factoring or the quadratic formula.

Front

What are the two numbers if the sum is 16 and the product is 15?

Back

The two numbers are 1 and 15.

Front

What are the two numbers if the sum is -25 and the product is 100?

Back

The two numbers are -20 and -5.

Front

In a diamond problem, what does the 'top' and 'bottom' refer to?

Back

In a diamond problem, the 'top' refers to the sum of the two numbers, and the 'bottom' refers to their product.

Front

If the top of a diamond problem is -4 and the bottom is 3, what are the two numbers?

Back

The two numbers are -3 and -1.

Front

What is the sum and product of the numbers 4 and -4?

Back

The sum is 0 and the product is -16.

Front

How can you verify the solution to a diamond problem?

Back

You can verify the solution by checking that the sum of the two numbers equals the given sum and that their product equals the given product.

Front

What is the significance of negative numbers in diamond problems?

Back

Negative numbers can be used in diamond problems, and they can affect both the sum and product. Understanding how to work with negative numbers is essential for solving these problems.

Front

What is the quadratic formula used for in relation to diamond problems?

Back

The quadratic formula is used to find the roots of a quadratic equation, which can be derived from the sum and product of two numbers in diamond problems.