To Solve the quadratic equation x^ 2 - ax + b = 0 using a ruler and compasses only.
Given : a line with the points Y and Z having coordinates (0,1) and (a,b) respectively.
1.Find the centre of the circle YZ by bisecting the diameter YZ in the usual manner.
2.Draw the circle with diameter YZ.
3.The circle YZ cuts the horizontal (X) axis at X1 and X2 with coordinates (x1,0) and (x2,0) where these are the roots of the original quadratic equation x^ 2 - ax + b = 0
It is an easy method ecause this method is so simple, but people prefer to use the algebraic method instead. That's because this method is so highly sensitive to the slightest inaccuracy in your drawing of the circle. 
