Question

If the solutions to an equation are 2 and –3, which of the following could be the equation?

Answer 1

All my work is shown in the image below.

Answer 2

For this case we must find an equation, whose solutions are given by:

`x = 2\\x = -3`

Or equivalently:

`(x-2) (x + 3) = 0`

Applying distributive property we have:

`x ^ 2 + 3x-2x-6 = 0\\x ^ 2 + x-6 = 0`

Now, if we multiply both sides of the equation by 2, we have:

`2x ^ 2 + 2x-12 = 0`

Thus, the equation that has the solution
`x = 2\ and\ x = -3` is:

`2x ^ 2 + 2x-12 = 0`

Answer:

`2x ^ 2 + 2x-12 = 0`

Option D