Quadratic Equation

If the equation x^2+ax+b=0 and x^2+px+q=0 have a common root,prove that (a-p)(bp-aq)=(b-q)^2
x^2+ax+b=0 and x^2+px+q=0 have a common root

x^2+ax+b=0
x^2=-ax-b

sub into x^2+px+q=0
-ax-b+px+q=0
(p-a)x=b-q
x=(b-q)/(p-a)

sub into x^2=-ax-b
[(b-q)/(p-a)]^2=-a[(b-q)/(p-a)]-b
(b-q)^2=-a(b-q)(p-a)-b(p-a )^2
(b-q)^2=(p-a)[-a(b-q)-b(p-a)]
(b-q)^2=(p-a)(-bp+aq)
(a-p)(bp-aq)=(b-q)^2.