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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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