what two numbers multiply to -56 and add up to 10
The Correct Answer and Explanation is:
Correct Answer:
The two numbers are 14 and –4.
Check:
- 14 × (–4) = –56 ✔
- 14 + (–4) = 10 ✔
Explanation (Textbook Style):
In algebra, we often encounter problems that ask us to find two numbers based on their product and their sum. These types of problems are commonly used when factoring quadratic trinomials, solving equations, or working with number puzzles.
In this case, we are given two conditions:
- The product of two numbers is –56
- The sum of the same two numbers is 10
To solve this, we need to think of factor pairs of –56, because we are looking for two numbers that multiply to give –56. Since the product is negative, one number must be positive and the other must be negative.
Let’s list all factor pairs of –56 and check their sums:
- 1 and –56 → 1 + (–56) = –55
- –1 and 56 → –1 + 56 = 55
- 2 and –28 → 2 + (–28) = –26
- –2 and 28 → –2 + 28 = 26
- 4 and –14 → 4 + (–14) = –10
- –4 and 14 → –4 + 14 = 10 ✔
- 7 and –8 → 7 + (–8) = –1
- –7 and 8 → –7 + 8 = 1
Out of all these combinations, only –4 and 14 add up to 10, while still multiplying to –56. This means these are the correct two numbers.
Thus, 14 and –4 are the numbers that satisfy both conditions.
This method of trial and error with factor pairs is a reliable and structured approach when solving problems involving a target sum and product.
