Let $a$ and $b$ be positive real numbers. For each of the equations
$$\begin{aligned} & ax^{2} - 2x + b = 0 \\ & bx^{2} - 3bx + a = 0 \end{aligned}$$
the sum of roots is 1 more than the product of roots.
Which of the following could be the quadratic equation whose roots are $a$ and $b$?
A) $9x^{2} + 8x + 18 = 0$ B) $9x^{2} - 14x + 8 = 0$ C) $9x^{2} - 18x + 14 = 0$ D) $9x^{2} - 8x + 14 = 0$ E) $9x^{2} - 18x + 8 = 0$