Question

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

Answer 1

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:

Let's start with the roots:

`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:

`(x-3)(x+4)=0`

We can now distribute out the 2 quantities:

`x^2+x-12=0`