Copy of Roots of the quadratic equation: a geometric approach
Given the quadratic equation , to find the roots geometrically. Draw the points and , and let the line joining these two points cut the unit circle with centre (0, 1) in points A and B. Project A and B from the point (0, 2) onto the x-axis at the points A' and B'. Then A' and B' are the roots of the given quadratic equation. (Karl G. C. von Staudt 1798-1867)
Prove the theorem