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## Main Question or Discussion Point

I remember back when I did a lot of quadratic equations, occasionally I had to find an unknown coefficient and if I remember correctly, generally I had to use the discriminant which gave me another quadratic which I could then use to solve for the coefficient.

My question is why does this work? Why can the discriminant be used in this way?

My question is why does this work? Why can the discriminant be used in this way?