Which 2 numbers have a sum of 5 and product of -14

Question

Multiplying negative numbers and addimg negative numbers to get answers

 

Answer 1

a + b = 5

ab = -14

 

Okay, just by looking at it, the numbers are 7 and -2, because after all, 7 * 2 = 14. If we subtract 2 from 7, then that gives 5. But you're probably needing to show actual work, aren't you? Vey well. Isolate one of the variables:

a = 5 - b

Substitution:

b(5 - b) = -14

Distribute:

-b² + 5b = -14

Move everything to form a quadratic:

0 = b² - 5b - 14

Factor:

0 = (b - 7)(b + 2)

That gives us:

0 = b - 7 or b + 2

b = 7 or -2

And if b is one of the numbers, a has to be the other.