The product of two consecutive positive integers is 342. Represent in the above situation in the form of quadratic equation. Find the numbet also.

18 and 19

Step-by-step explanation:

Consecutive positive integers have a difference of 1 between them

let n and n + 1 be the 2 integers, then

n (n + 1) = 342, that is

n² + n = 342 (subtract 342 from both sides)

n² + n - 342 = 0 ← quadratic equation in standard form

(n + 19) (n - 18) = 0 ← in factored form

Equate each factor to zero and solve for n

n + 19 = 0 ⇒ n = - 19

n - 18 = 0 ⇒ n = 18

However, n > 0 ⇒ n = 18 and n + 1 = 18 + 1 = 19

The 2 integers are 18 and 19