How do you write a quadratic equation with given root(s) 3, -4?

It's like solving a quadratic, but in reverse, and in this case you'll arrive at ${x}^{2} + x - 12 = 0$

Explanation:

We're going to go "backwards" with this problem - normally we're asked to take a quadratic equation and find the roots. So we'll do what we normally do, but in reverse:

$x = 3$, $x = - 4$

So let's move the constants over with the x terms to have equations equal to 0:

$x - 3 = 0$, $x + 4 = 0$

Now we can set up the equation, as:

$\left(x - 3\right) \left(x + 4\right) = 0$

We can now distribute out the 2 quantities:

${x}^{2} + x - 12 = 0$