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

Let the two numbers be x and 27 – x so that their sum is 27

Product = 182

⇒ x(27 – x) = 182

⇒ 27x – x² = 182

⇒ x² – 27x + 182 = 0

⇒ x² – 14x – 13x + 182 = 0

taking x common from first two terms and – 13 common from next two

⇒ x(x – 14) – 13(x – 14) = 0

⇒ (x – 13)(x – 14) = 0

⇒ (x – 13) = 0 or (x – 14) = 0

Therefore x = 13 and x = 14

Take any value of x 13 or 14 if we subtract it from 27 we get the other value 13/14

Hence the numbers are 13 and 14 whose sum is 27 and product is 182