Let A = (0,1) and B=(-p/2,(q+1)/2) be tw...

Let `A = (0,1) and B=(-p/2,(q+1)/2)` be two fixed points in a plane. Let C denote a circle with centre B and passing through A. Prove that the real roots of the equation `x^2 + px + q = 0` are given by the abscissae of the points of intersection of C with the x-axis.

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