Question

Need help finding numbers/equations that are equal to 12 and 116

Answer 1

Quadratic equations can have two solutions, then, we can build one whose 2 solutions are 12 and 116.

It can be built as follows:

`(x-12)(x-116)=0`

The equation is a product of two expressions equal to 0. When a product is 0, we know that either the first parenthesis or the second one is equal to 0. Then, the solution x for the above equation can be:

`\begin{gathered} (x-12)=0 \\ x=12 \end{gathered}`

Or well:

`\begin{gathered} x-116=0 \\ x=116 \end{gathered}`

Both 12 and 116 solve the equation. We can rewrite the equation by solving the multiplication:

`\begin{gathered} (x-12)(x-116)=0 \\ x^2-12x-116x+12\cdot116=0 \\ x^2-128x+1392=0 \end{gathered}`

Then, an equation that has as solutions both 12 and 116 could be:

`x^2-128x+1392=0`

If we plug either value on the x of the equation we will see that the equality is fulfilled. Alternatively, if we solve the quadratic equation with the general formula, we will also obtain that the x can take the values of both 12 and 116