2x^2 – 3x – 7 = 0

If c and d are the two solutions of the quadratic equation above, what is the value of c + d?

Is there a smarter/quicker way to solve this than the quadratic formula?

Yes and no. Which is to say, you should use the quadratic formula, but you don’t have to take it all the way. The two solutions you get when you do the quadratic formula come from the in . But in this case, since we’re adding the two solutions, everything after the will cancel out! Let’s say and are the “plus” and “minus” solutions, respectively. Then we can say:

That’s a lot easier to work with, right?

## Comments (2)

You could also just know how to us the special formula/“trick”. The sum of solutions is -b/a, and the product of solutions is c/a!

Note: This only works if the problem is in quadratic form (ax^2 + bx + c)