Verify the Equation A(B) = c/a

Let A and B be roots of the quadratic equation ax^2 + bx + c = 0.
Verify the statement A(B) = c/a.

ax^2 + bx + c = 0
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x = (1/2*a)*(-b +/- sqrt(b^2 - 4*a*c))

A = (1/2*a)*(-b - sqrt(b^2 - 4*a*c))
B = (1/2*a)*(-b + sqrt(b^2 - 4*a*c))

A*B = (1/(4*a^2))*((-b - sqrt(b^2 - 4*a*c))*(-b + sqrt(b^2 - 4*a*c)))
= (1/(4*a^2))*(b^2 - (b^2 - 4*a*c))
= (1/(4*a^2))*(4*a*c)
= c/a <<<