Roots of the quadratic equation: a geometric approach
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Given the quadratic equation [math]x^2 - r\,x + s = 0[/math], to find the roots geometrically. Draw the points [math]C = (s/r, 0)[/math] and [math]D = (4/r, 2)[/math], and let the line joining these two points cut the unit circle with centre (0, 1) in points [i]A[/i] and [i]B[/i]. Project [i]A[/i] and [i]B[/i] from the point (0, 2) onto the x-axis at the points [i]A'[/i] and [i]B'[/i]. Then [i]A'[/i] and [i]B'[/i] are the roots of the given quadratic equation. (Karl G. C. von Staudt 1798-1867) |
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Prove the theorem |