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

1 Answer

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#