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.

Answer 1

Let two positive consecutive positive integers are n & n+1.

then,

$n(n+1)=306$

$n^2+n-306=0$ ________ (1)

Equation (1) is required quadratic equation

$n^2+18n-17n-306=0$

$n(n+18)-17(n+18)=0$

$(n+18)(n-17)=0$

n=-18,17

But n is positive

So, n=17

Therefore, Two consecutive positive integer are 17,18