The quadratic equation Ax^2 + Bx + C = 0 factors into linear factors with integer coefficients. Prove that the quadratic Ax^2 + 2Bx + 4C also factors into linear factors with integer coefficients. How do do the roots of Ax^2 + 2Bx + 4C = 0 relate to the roots of Ax^2 + Bx + C = 0?
