Quadratic+Equations+with+no+rational+roots

//i// itself was formed when mathematicians thought that there was no value which x could be so that the equation, //X// 2 = -1. works. However, now that we know that i is the square root of -1, we can solve quadratic equations leaving complex solutions. For example, take this equation, //X// 2 -2x + 2 = 2

After substituting this into the quadratic formula, we end up with:

After simplifying the surd, we find that we need the square root of -12 Obviously, this, using rational numbers, is impossible. This is where //i// comes into play...