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# Represent the following situations in the form of quadratic equations:

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

Given:

The product of two consecutive positive integers is $306$.

To do:

Here, we have to find the integers.

Solution:

Let the two consecutive integers be $x$ and $x+1$, where $x$ is the smaller integer.

Therefore,

$x(x + 1) = 306$

$x^2 + x – 306 = 0$

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

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

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

$x+18=0$ or $x-17=0$

$x=17$ or $x=-18$

This implies,

If $x=17$ then $x+1=17+1=18$

If $x=-18$ then $x+1=-18+1=-17$

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