Question

The product of two consecutive natural number is $240$. Find the number.

Answer 1

Let the two consecutive natural number be $x;(x+1)$

Given $x(x+1)=240$

$\Rightarrow x^2+x-240=0$

Comparing with the general form of quadratic equation $a{x}^2+bx+c=0$

We have, $a=1,b=1,c=-240$

Roots are given by :

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

$x=\frac{-1\pm \sqrt{1^2-4\cdot 1\cdot (-240)}}{2\cdot 1}$

$x=\frac{-1\pm \sqrt{961}}{2}$

$x=\frac{-1\pm 31}{2}$

$x=-16or15$

Since natural number can't be negative, only $x=15$ is considered.

Therefore two consecutive natural number is $15,16$