The following geometric method for solving quadratic equations of the form x2 − ax + b = 0...

The following geometric method for solving quadratic equations of the form x2 − ax + b = 0 is due to the British writer Thomas Carlyle (1795–1881):

To solve the equation x2 − ax + b = 0, plot the points A(0,1) and B(a, b). Then draw the circle with as diameter. The x-intercepts of this circle are the roots of the equation.

Use the techniques of this chapter to verify for yourself that this method indeed yields the roots for the equation x2 − 6x + 5 = 0. (You need to find the equation of the circle, determine the x-intercepts, and then check that the numbers you obtain are the roots of the given equation.) After you have done this, carefully write out your verification in detail (using complete sentences), as if you were explaining the method to a classmate. Be sure to make explicit reference to any formulas or equations that you use from the chapter.