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\[x = (-b \pm \sqrt(b^2 - 4ac))/2a\] that is the quadratic formula. It states that for any Quadratic of the form \[ax^2 + bx + c = 0\] that x has two possible roots(real or imaginary). the portion under the square root \[b^2 - 4ac\]is known as the "descriminant" because it states whether the roots will be complex or imaginary. If the descriminant is negative then the root will be imaginary, if it is positive then the root is real. Now it is possible that the descriminant could be 0, in which case there is one root known as a double root. This is when the curve just touches the x axis at a single point, and thus the x-axis is a tangent to the curve. The reason that the equation is as it is has to do with its derivation. Partly it states that the minimum, or maximum of a quadratic is at the point where \[x = -b/2a\] and that the distance between the two roots from this minimum is equal in magnitude and opposite in direction. This distance is always \[ \sqrt(b^2-4ac)/2a\]. Thus the two roots will be the coordinate of the mimimum or maximum by a distance of that in both directions along the x-axis.