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

Question

asked Sep 9, 2020 71.9k views

2 Answers

Jack Carlisle · Answer 1 · 2020-09-15T02:17:03+0000

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:

Option D