QuestionWrite two numbers that multiply to the value on top and add to the value on bottom.

Studdy Solution

STEP 1

1. We are looking for two numbers, say $a$ and $b$ , such that their product is $-16$ and their sum is $-6$ .
2. The problem is a typical example of factoring a quadratic expression or solving a system of equations involving sum and product.

STEP 2

1. Set up equations based on the given conditions.
2. Solve the system of equations to find the two numbers.

STEP 3

Set up the equations based on the problem statement. We need two numbers $a$ and $b$ such that:
$a \times b = -16$ $a + b = -6$

STEP 4

To solve for $a$ and $b$ , consider possible pairs of factors of $-16$ . The factors of $-16$ can be $(-1, 16), (1, -16), (-2, 8), (2, -8), (-4, 4), (4, -4)$ .

STEP 5

Check each pair to see which one adds up to $-6$ :
- For $(-1, 16)$ , the sum is $-1 + 16 = 15$ . - For $(1, -16)$ , the sum is $1 - 16 = -15$ . - For $(-2, 8)$ , the sum is $-2 + 8 = 6$ . - For $(2, -8)$ , the sum is $2 - 8 = -6$ . - For $(-4, 4)$ , the sum is $-4 + 4 = 0$ . - For $(4, -4)$ , the sum is $4 - 4 = 0$ .

STEP 6

Identify the correct pair. The pair $(2, -8)$ satisfies both conditions:
$2 \times (-8) = -16$ $2 + (-8) = -6$
The two numbers that multiply to $-16$ and add to $-6$ are $2$ and $-8$ .

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