Question

What pair of numbers multiplies to -168 and adds to 10?

a) 18 and −8
b) −14 and 12
c) 14 and 12
d) −14 and−12

Answer 1

To find the pair of numbers that multiplies to -168 and adds to 10, we can set up a quadratic equation. Let the two numbers be x and y. Using the second equation, we can solve for x and substitute it into the first equation. By factoring, we find that the pair of numbers is 18 and -8.

Step-by-step explanation:

To find the pair of numbers that multiplies to -168 and adds to 10, we can set up a quadratic equation. Let the two numbers be x and y. The equation will be:
x * y = -168
x + y = 10

Using the second equation, we can solve for x and substitute it into the first equation:
x = 10 - y
(10 - y) * y = -168

Expanding the equation and simplifying, we get:
y² - 10y - 168 = 0

Now we can factor or use the quadratic formula to solve for y. By factoring, we find that the pair of numbers is:
(y - 18) * (y + 8) = 0
y = 18 or y = -8

Therefore, the pair of numbers that multiplies to -168 and adds to 10 is 18 and -8. So, the correct answer is a) 18 and -8.