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

let the two numbers be x and y

According to the given condition

x + y = 27 ⇒ y = 27 - x

And x × y = 182

⇒ x (27 –x) = 182

⇒ 27x – x² - 182 = 0

⇒ x² – 27x + 182 = 0

⇒ x² – 13x – 14x + 182 = 0

⇒ x (x - 13) - 14 (x - 13) = 0

⇒ (x - 14) (x - 13) = 0

The roots of the equation are those value for which(x - 14) (x - 13) = 0

⇒ x = 14 or 13

Hence two numbers are 14 and 13