The sum of two numbers is 5; their product is 14. Find the numbers.
Correct Option:
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
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