Question

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

Answer 1

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

Answer 2

All my work is shown in the image below.