MathematicsFind 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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