Verify the Given Math Statement

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

Note that x^2 + b/a x + c/a = 0

Then if A and B are roots, the expression factors as (x - A)(X - B)

(x - A)(X - B) = x^2 + b/a x + c/a

Expand: x^2 - Ax - Bx + AB = x^2 + b/a x + c/a

x^2 - (A + B)x + AB = x^2 + b/a x + c/a

Equate the coefficients on the x-term: -(A + B) = b/a --> A + B = -b/a

(x-A)(x-B)=x^2-(A+B)x+AB

ax^2 + bx + c = 0
x^2+b/a*x+c/a=0

By comparison: -(A+B)=b/a
i.e. A+B=-b/a QED