CAT (QA) PYQs

If $(3+2\sqrt{2})$ is a root of the equation $ax^2 + bx + c = 0$, and $(4+2\sqrt{3})$ is a root of the equation $ay^2 + my + n = 0$, where $a, b, c, m$ and $n$ are integers,
then the value of $(\frac{b}{m} + \frac{c-2b}{n})$ is

The equation $x^3 + (2r + 1)x^2 + (4r - 1)x + 2 = 0$ has $- 2$ as one of the roots. If the other two roots are real, then the minimum possible non-negative integer value of $r$ is

The quadratic equation $x² + bx + c = 0$ has two roots $4a$ and $3a,$ where a is an integer. Which of the following is a possible value of $b² + c$?