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 \pm in x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}. But in this case, since we’re adding the two solutions, everything after the \pm will cancel out! Let’s say c and d are the “plus” and “minus” solutions, respectively. Then we can say:


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

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