Question

The product of two consecutive positive integers is 306. Form the quadratic equation to find the integers, if x denotes the smaller integer.

Answer 1

Let the first integer number = x

Next consecutive positive integer will = x+1

Product of both integers = x$\times$(x+1)=306

$x^2+x=306$

⇒$x^2+x-306=0$..........this is the required quadratic equation.

We can further solve this equation to find out the roots of this quadratic equation by splitting the middle term.

⇒$x^2+18x-17x-306=0$

⇒$x(x+18)-17(x+18)=0$

⇒$(x+18)(x-17)=0$

Either x+18=0 or x−17=0

⇒x=−18 or x=17

Since integers are positive x can only be 17

∴x+1=17+1=18

Therefore, two consecutive positive integers will be 17 and 18.