Question

What two numbers multiply to get -48 add to 4

Answer 1

2 -
`√(52)` and 2 +
`√(52)`

Explanation:

let the 2 numbers be x and y , then

x + y = 4 ( subtract x from both sides )

y = 4 - x → (1)

xy = - 48 → (2)

substitute y = 4 - x into (2)

x(4 - x) = - 48

4x - x² = - 48 ( multiply through by - 1 )

x² - 4x = 48

solve using the method of completing the square

add ( half the coefficient of the x- term )² to both sides

x² + 2(- 2) x + (- 2)² = 48 + (- 2)²

(x - 2)² = 48 + 4 = 52 ( take square root of both sides )

x - 2 = ±
`√(52)` ( add 2 to both sides )

x = 2 ±
`√(52)`

substitute this value into (1)

y = 4 - (2 ±
`√(52)` ) = 4 - 2 ±
`√(52)` = 2 ±
`√(52)`

then the 2 numbers are

2 -
`√(52)` and 2 +
`√(52)`

Answer 2

Answer: -12 x 4

Explanation:

12 times 4 is 48

Rule: A negative multiplied by a positive, will always give you a negative.

So, -12 is a negative number and 4 is a positive number.

Negative x Positive = Negative

Positive x Negative = Negative

-12 x 4 = -48