Find two numbers whose sum is 27 and product is 182.

# Find two numbers whose sum is 27 and product is 182.

1. A
10,7
2. B
13,14
3. C
19,8
4. D
None of these

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### Solution:

Let us consider one of the numbers to be x. Then the other number will be 27 - x.
The product of the two numbers is given as 182
This can be written in the form of the following quadratic equation:
x(27 - x) = 182
x(27 - x) = 182
27x - x2 = 182
27x - x2 - 182 = 0
x2 - 27 x + 182 = 0 [Rearranging the terms and multiplying both sides by negative sign]
x2 - 14x - 13x + 182 = 0
x (x - 14) - 13 (x - 14) = 0
(x -13) (x - 14) = 0
x - 13 = 0 and x - 14 = 0
x = 13 and x = 14
Therefore, the required numbers are 13, 14.
So, Option 2 is correct.

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