Question

The product of two consecutive integers is 90 find the two integers then check your answer?

Answer 1

Let n be the integer. Then, we can write the following equation

`n(n+1)=90`

which is equal to

`n^2+n-90=0`

We can solve this quadratic function by applying the quadratic formula:

`n=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a}`

where in our case a=1, b=1 and c= -90. By substituting these values into the last formula, we get

`n=\frac{-1\pm\sqrt[]{1^2-4(1)(-90)}}{2(1)}`

then, we have

`\begin{gathered} n=\frac{-1\pm\sqrt[]{1+360}}{2} \\ n=\frac{-1\pm\sqrt[]{361}}{2} \\ n=(-1\pm19)/(2) \end{gathered}`

Then, the first solution is

`\begin{gathered} n=(-1+19)/(2) \\ n=(18)/(2) \\ n=9 \end{gathered}`

and the second solution is

`\begin{gathered} n=(-1-19)/(2) \\ n=-(20)/(2) \\ n=-10 \end{gathered}`

Then, we have the following solutions:

- Negative integer: n= - 10

- Positive integer: n=9