The sum of two numbers is 5; their product is -14. Find the numbers.

A.

x = 5 or 1

B.

x = 7 or 1

C.

x = 7 or 0

D.

x = 7 or − 2

Correct answer is D

Let x represent the first number;

Then, the other is (5 − x) , since their sum is 5 and their product is 14

x(5 − x) = 14

5x − x2 = 14

x2 − 5x − 14 = 0

(x2 − 7x) + (2x − 14) = 0

x(x − 7) + 2(x − 7) = 0

(x − 7)(x + 2) = 0

Either (x − 7) = 0 or (x + 2) = 0

x = 7 or x = − 2

The two numbers are 7 and − 2