Question

Represent the following situation in the form of a quadratic equation:

The product of two consecutive positive integers is 306. We need to find the integers.

The product of two consecutive positive integers is 306. Find the integers.

Answer 1

Let the first integer number = x

Next consecutive positive integer will = x + 1

Product of both integers = x × (x +1) = 306

⇒ x² + x = 306

⇒ x² + x - 306 = 0

⇒ 2x² + 18x - 17x - 306 = 0

⇒ x(x + 18) - 17(x + 18) = 0

⇒ (x + 18)(x - 17) = 0

⇒ x + 18 = 0 and x - 17 = 0

⇒ x = -18 and x = 17

Since,

First positive integer = x = 17

Second positive integer = x + 1

= 17 + 1

= 18